Ernesto Che Guevara – Lavretsky

In this post, we will see the biography of Ernesto “Che” Guevara by I. R. Lavretsky.  Che perhaps is the most iconic face of a revolutionary, and indeed in deed he was a revolutionary at heart till his untimely and gruesome death.


About the book:

This book by I. R. Lavretsky, Dr. Sc. (Hist.), Is concerned with the life and activities of the outstanding revolutionary and fighter for the national liberation of the Latin American peoples Ernesto Che Guevara. The author makes use of numerous documents, press Items, notes from personal conversations with friends, relatives and comrades-in-arms of Che Guevara, as well as a wealth of photographs.

The book was translated from the Russian by A. B. Eklof and was designed by V. An. The book was first published by Progress Publishers in 1976.

Original scan by IA user Thomas Mrett. We cleaned, OCRed, bookmarked the scan.

The Internet Archive link.




First Steps

Character Formation

A Lost Battle

The “Granma”


Fighting in the Mountains

The Daily Life of a Guerrilla

Through Santa Clara to Havana


In the Whirlwind of Revolution

The World of Socialism

A Shock Worker for Communism

“Cuba Si, Yanqui No!”


A Mysterious Disappearance

The Camp on the Nancahuasu River

And Again the Thunder of Battle

On the Other Side of the Barricades

The Immortal Cause of Revolution


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The Principles of Philosophy – Rakitov

In this post, we will see the book The Principles of Philosophy by Anatoly Rakitov.


About the book:

The structure of this book permits the student to read and master its matter in varying order according to the aims and purposes he or she is pursuing. The introduction “What Is Philosophy?” provides basic information about philosophy, its subject-matter and methods, the main points that distinguish it from other disciplines, and its place in the system of Marxism-Leninism. This chapter also contains information on the origin and various stages in the evolution of philosophy, and singles out the main matters that will subsequently be discussed. These problems will be treated in more detail in the following chapters, the material being arranged in order of increasing difficulty. Each of the successive chapters depends on the preceding ones. For the reader’s better assimilation of the proofs and arguments by which the superiority of materialism over idealism, of dialectics over metaphysics, and of Marxist-Leninist philosophy over other philosophical schools and currents is demonstrated, the text includes dialogues and talks between imaginary persons who express different points of view. These dialogues should be read and studied as attentively as the basic text.

The book was translated from the Russian by H. Campbell Creighton and was first published in English by Progress Publishers in 1989. This book is a part of the series Student’s Library in which many books were published especially pertaining to philosophy and sociology within the framework of dialectical-materialism.

Original scan by IA user Thomas Mrett. We cleaned, OCRed, bookmarked the scan.

The Internet Archive link.



How to Use This Book 7

Introduction 9

What Is Philosophy 9

Who Needs Philosophy? And Why? 9

001 Man in the Modern World 9

002 “The Intellectual Quintessence of Its Time” 10

003 Philosophy and World Outlook 12

004 Philosophy and the General Methodology of Activity and Cognition 13

005 Philosophy and Ideology 16

006 The Main Task of Marxist-Leninist Philosophy 20

The Basic Question. The Subject Matter and Method of Philosophy 22

007 The Basic Question of Philosophy 22

008 The ‘ First Aspect of the Basic Question of Philosophy. Idealism and Materialism 24.

009 A Dialogue of a Materialist and an Idealist 26

010 The Second Aspect of the Basic Question of Philosophy 30

011 A Dialogue about the Knowability of the World 31

012 The Method of Philosophy; the Preliminary Concept of Dialectics and Metaphysics 34.

013 The Subject Matter of Marxist-Leninist Philosophy 36

014 The Principle of Partisanship in Philosophy 37

The Origin and Development of Philosophy 39

015 The Philosophy of Antiquity 39
016 The Philosophy of the Orient 41
017 The Philosophy of the Middle Ages 42
018 The Philosophy and Culture of the Renaissance 43
019 The Philosophy of Bourgeois Society 44
020 The Philosophical, Social, and Scientific Prerequisites of Marxian Philosophy 46

021 The Rise of Dialectical Materialism: a Radical Turn in the Development of Philosophy 49
022 A New Stage in the Development of Marxist Philosophy 51


Chapter I
Matter and Consciousness

Matter and the Picture of the World 56

101 Notion and Category 56
102 What Is Matter? 57
103 How Views of Matter Developed 59
104 The Contemporary Scientific Picture of the World 62
105 The Material Unity of the World 65
106 System, Structure, Element 65
107 Necessity and Chance 68
108 Laws of the Objective World 70.

Motion, Time and Space 74

109 Matter and Motion 74
110 Dialogue on Motion and Rest 76
111 Form and Content 77
112 The Forms of the Motion of Matter 79
113 Time and Space 81
114 The Irreconcilability of the Idealist and Materialist Conceptions of Time and Space 82
115 Modern Scientific Notions of Time and Space 84
116 Cause and Effect 85

Reflection as a General Property of Matter 88

117 The Basic Question of Philosophy in the “Computer Age” 88
118 What Is Reflection? 89
119 Reflection in the Inorganic World 90
120 The Complication of Reflection during the Transition to Animate Nature 92
121 The Evolution of Life and Origin of the Nervous System 93
122 Active and Passive Reflection of Reality 95
123 The Psychic and the Physical, the Ideal and the Material 97

Human Consciousness 101

124 The Brain as the Material Organ of Mental Activity 10l
125 Work as the Basis of Consciousness 102
126 Language and Thought 104
127 On the Relative Character of the Opposition of Matter and Consciousness 106
128 Can Computers Think? 108
129 Some Conclusions. The Synthesising Function of Philosophy 111

Chapter II

Social Being and Social Consciousness 114

The Materialist Conception of Society and Its History 114

201 A Talk about the Idealist and Materialist Conceptions of Society 114
202 Man and Activity. Preconditions for the Materialist Conception of History 116
203 The Development of Society &s a NaturalHistorical Process 118
204 The Mode of Production as the Basis of the Development and Functioning of Society 120
205 Basis and Superstructure 125
206 Classes and Class Struggle 127
207 The State in the System of the Superstructure 130
208 Political Parties in the System of the Superstructure 134
209 Social Organisations in the System of the Superstructure 137
210 Social Being and Social Consciousness 139
211 The Basic Principle of Historical Materialism 142

The Theory of SocioEconomic Formation 144

212 The Individual, Particular, and Universal 144
213 What Is a SocioEconomic Formation? 146
214 Social Revolution 148
215 The Structure of a Social Revolution 149
216 The Forming of Human Society 151
217 The Primitive Communal Formation 152
218 The SlaveOwning Formation 154
219 The Feudal Formation 156
220 The Capitalist Formation 158
221 The Communist Formation 161
222 The Category “SocioEconomic Formation” and Historical Reality 164

The Functions and Forms of Social Consciousness 166

223 Social Consciousness and the Development of Society 166
224 Ideology in the System of Social Consciousness 168
225 Social Psychology and Everyday Consciousness 170
226 Political Consciousness and Politics 172
227 Legal Consciousness and Law 174
228 Morality as a Form of Social Consciousness 176
229 Economic Consciousness 179
230 Religion as a Form of Social Consciousness 181
231 Artistic Consciousness and Art 183
232 Individual and Social Consciousness 187
233 On the Relative Independence of Social Consciousness 189
234 Growth of the Role of the Subjective Factor under Socialism 192

Chapter III

Nature and Society 196

On the Relationship of Nature and Society 196

301 Nature and Society 196
302 Dialogue about Nature and Society 198
303 PreMarxian Views on Nature and Society 201
304 Dialectical Materialism on the Relation of Nature and Society 203.

The Environment. The Biological and Social in Social Development 205

305 The Structure of the Environment 205
306 Mankind and the Natural Environment 206
307 The Biological and Social in Man 209
308 Races and Nations 211
309 The Role of Population in the Development of Society 216
310 The Artificial Habitat 220

Nature and Society in the Age of Scientific and Technological Progress 222

311 What Is Scientific and Technological Progress or the Scientific and Technical Revolution? 222
312 Scientific and Technical Progress and Its Consequences under Capitalism and Socialism 226
313 Ecological Consciousness and Ideological Struggle 230

Chapter IV

The Main Laws of Dialectics 234

The Sources of Development 234

401 The Idea of Development 234
402 What Is the Source of Development? 237
403 The Categories of “Opposition” and “Contradiction” 239
404 The Unity and Mutual Conversion of Opposites 241
405 The Struggle of Opposites and Resolution of Contradictions: the Source of Development 244
406 Forms of Contradictions 247
407 The Resolution of Contradictions in Socialist Society 252
408 The Law of the Unity and Struggle of Opposites: the Essence and Core of Dialectics 255

Forms of Development 257

409 On the Form of Development 257
410 A Dialogue about the Continuous and Intermittent, the Gradual and Sudden in the Process of Development 257
411 Quantity, Quality, Measure, and Leap 260
412 Evolution and Revolution 263
413 The Dialectic Connection between Quantitative and Qualitative Changes 266
414 The Law of the Transition of Quantitative Changes into Qualitative, and Vice Versa 270
415 Quantitative and Qualitative Changes in the Structure of the Socialist Revolution 271
416 The Dialectic of Quantity and Quality in the Present Stage of the Development of Socialism 274

The Direction of Development 417

A Dialogue on the Direction of Development 277
418 The Spiral Like Character of Development 278
419 Dialectical Negation and Continuity 279
420 Possibility and Actuality 283
421 The Dialectic of the Possible and the Real in a Revolutionary Situation 285
422 What Is Social Progress? 286
423 The Dialectical Law of the Negation of Negation 289

Chapter V

The Theory of Knowledge 291

The Dialectics of Knowing 291

501 What Does It Mean to Know? 291. 502 Cognition as Reflection 293. 503 A TalJ… about the Sources of Knowledge · 294. 504 The Role of Sensation in Knowing 298. 505 The Role of Abstraction in Knowing. The Method of the Ascent from the Abstract to the Concrete 300. 506 The Epistemological Roots of Idealism 304. 507 What Is Truth? 305. 508 The Role of Practice in Knowing 309. 509 Appearance and Essence. The Dialectics of Knowing 311.

The Forms and Methods of Scientific Cognition.

510 Theory and Hypothesis 314
511 Experiment and Observation in Scientific Cognition 318
512 Certain General Scientific Methods of Cognition 320
513 Models and Modelling in Scientific Cognition 326
514 The Application of Mathematics and Modern Science 327
515 Science and Society 329.

Chapter VI

Man and Society

601 A Chat on the Essence of Man and the Sense of Life 333
602 Freedom and Necessity 338
603 The Role of the Individual and of the Masses in the Development and Life of Society 342
604 The Individual and the Masses in Socialist Society 346
605 Socialist Democracy and Communist Education 348
606 Acceleration of Socio-Economic Progress. Reorganisation (Perestroika) and the Human Factor 351
607 The Road to a New Civilisation 353
608 The Struggle for Peace and the Destiny of Humankind 356
609 Predicting the Future 359

A Last Chat with the Reader 363

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Vector Aanalysis – Krasnov, Kiselev, Makarenko

In this post, we will see the book Vector Analysis by  M.L. Krasnov, A.I. Kiselev,   G.I. Makarenko.



About the book:

The present collection of problems in vector analysis contains the required minimum of problems and exercises for the course of vector analysis of engineering colleges.

Each section starts with a brief review of theory and detailed solutions of a sufficient number of typical problems. The text contains 100 worked problems and there are 314 problems left to the student. There are also a certain number of problems of an applied nature that have been chosen so that their analysis does not require supplementary information in specialized fields. The material of the sixth chapter is devoted to curvilinear coordinates and the basic operations of vector analysis in curvilinear coordinates. Its purpose is to give the reader at least a few problems to develop the necessary skills.

The exposition in this text follows closely the lines currently employed at the chair of higher mathematics of the Moscow Power Institute.

The present text may be regarded as a short course in vector analysis in which the basic facts are given without proof but with illustrative examples of a practical nature. Hence this problem book may be used in a recapitulation of the essentials of vector analysis or as a text for readers who wish merely to master the techniques of vector analysis, while dispensing with the proofs of propositions and theorems.

This collection of problems is designed for students of day and evening departments at engineering colleges and also for correspondence students with a background of vector algebra and calculus as given in the first two years of college study.

The book was translated from the Russian by George Yankovsky and was first published by Mir in 1983.

All credits to the original uploader.

The Internet Archive link.


Preface 7

Sec. 1. The hodograph of a vector function 9
Sec. 2. The limit and continuity of a vector function of a scalar argument 11
Sec. 3. The derivative of a vector function with respect to a scalar argument 14
Sec. 4, Integrating a vector function of a scalar argument 18
Sec. 5. The first and second derivatives of a vector with
respect to the arc length of a curve. The curvature of a curve. The principal normal. 27
Sec. 6. Osculating plane. Binormal. Torsion. The Frenet formulas. 31

Sec. 7. Examples of scalar fields. Level surfaces and level linea 35
Sec. 8. Directional derivative 39
Sec. 9. The gradient of a scalar field 44

Sec. 10. Vector linea. Differential equations of vector linea 52
Sec. 11. The flux of a vector field. Methods of calculating flux 58
Sec. 12. The flux of a vector through a closed surface. The Gauss-Ostrogradsky Theorem. 89
Sec. 13. The divergence of a vector field. Solenoidal fields. 89
See. 14. A line integral in a vector field. The circulation of a vector field 96
Sec. 15. The curl (rotation) of a vector field 108
Sec. 16. Stokes’ theorem 111
Sec. 17. The independence of a line integral of the path
of integration. Green’s formula 115

See. 18. The criterion for the potentiality of a vector field t2t
See. 19. Computing a line integral in a potential field 124

See. 20. The Hamiltonian operator del 130
See. 21. Second-order differential operations. The Laplace operator 135
See. 22. Vector potential 146

See. 23. Curvilinear coordinates 152
See. 24. Basic operations of vector analysis in curvilinear coordinates 156
See. 25. The Laplace operator in orthogonal coordinates 174


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The Forces of Nature – Grigoryev, Myakishev

In this post we, will see the  book The Forces of Nature by V. Grigoryev and G. Myakishev.


About the book:

This book is a popular description of the unity of the forces of nature for the general reader.
At present, all interactions between bodies in nature are thought to be ultimately due to the interaction of elementary particles and involve only four types of forces: universal gravitation, or gravitational forces, electromagnetic forces, nuclear forces and the so- called weak interactions.
This book describes the principal properties of these four types of force and their “sphere of action”, that is, the part they play in diverse natural processes that range from galaxies to the atomic nucleus and the mutual transformations of elementary particles. It includes the latest achievements of physics and gives a picture of the unresolved problems that confront science today.

About the authors:

The authors of this book are Candidates of Physico-mathematical sciences Vladimir Grigoryev and Gennady Myakishev. In 1948 they graduated from the Physics Department of Moscow University and completed their graduate studies in 1951. At present both are Associate Professors of the Moscow University Physics Department.
V. Grigoryev has published over twenty papers on problems of quantum field theory and has been particularly interested in particle formation via high- energy collisions. G. Myakishev has written a number of works on electronics and problems of the methodology of science, several elementary numerous textbooks on physics and articles for popular-science magazines.

There are some amazing line drawings to illustrate the topics.



The book was translated from the Russian by George Yankovsky and was first published by Mir in 1967.

PDF | OCR | Bookmarked | Cover | 358 pp. | 300 dpi (upscaled to 600 dpi)

The Internet Archive link



1. A Word About the Word “Force” 9

2. Forces in Mechanics 10

3. Is It Always Possible to Describe an Interaction by Forces? 15

4. The Unity of the Forces of Nature 22


1. From Anaxagoras to Newton 27

2. The Law of Universal Gravitation 31

3. Gravitation in Action 41

4. Geometry and Gravitation 53


I. What Forces Are Called Electromagnetic? 89

2. What Is an Electric Charge? 93

3. The Interaction of Stationary Electric Charges 99

4. The Interaction of Moving Electric Charges 107

5. Close-range Action or Action at a Distance? 116

6. What Is an Electric Field and a Magnetic Field? 123

7. Relationships Between Electric and Magnetic Fields 131

8. Electromagnetic Waves  143


1. How Do Electromagnetic Forces Manifest Themselves? 153

2. Forces, the Structure of Matter, the Equations of Motion 158

3. Electromagnetic Forces in Electrically Neutral Bodies 163

4. FreeChargesandCurrentsinNature 191

5. Electromagnetic Waves in Nature 213

6. Why Electromagnetic Interactions Take Up Most of This Book? 226

7. An Insertion with All the Rights of a Real Chapter .228


1. The Nucleus and Elementary Particles 249
2. Nuclear Interactions and How They Occur 258

3. The Transformation of Atomic Nuclei 268


1. The Disintegration of Elementary Particles and the Neutrino 285

2. The Charge and the Transformations of Elementary Particles 300

3. The Neutrino and the Evolution of the Universe 308

4. An Early Summary of What We Have Learned 314


1. What Are the Resonance Particles? .319

2. Systematics of the Elementary Particles 328

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The Races of Mankind – Nesturkh

In this post, we will see the book The Races of Mankind by M. Nesturkh.


About the book (from the Preface):

This present book, by Professor M. F. Nesturkh, is based on the methodological principles of Soviet anthropology and the factual data obtained by that science. The author connects the origin of the races with the origin of mankind as a whole and acquaints the reader with the present status of these two problems; he deals at length with the history of the formation, dissemination and mingling of individual anthropological (racial) types and their groups, uses facts to expose the reactionary nature of racism and proves that it has no foundation in science.

Professor Nesturkh naturally devotes greater attention to anthropology proper, but he makes extensive use of other natural and social sciences-comparative anatomy, physiology, palaeontology, archaeology, ethnography, psychology, and linguisticsin accordance with Frederick Engels’s well-known postulate that anthropology is the transition from the morphology and physiology of man and his races to history.

It must not be thought that Professor Nesturkh’s book is limited to an exposure of racism. The problems dealt with are of a much broader cognitive significance. Among other things the reader will find the latest information on the anthropoids of the Tertiary period (the distant ancestors of man and the modern anthropoid apes), the earliest hominids (Pithecanthropus and Sinanthropus), Neanderthal man and the fossil men of the modern type. The author also deals with the natural selection of the earliest men, geographical isolation, inter-racial crossing, the times and places in which the great races were formed, the ways in which they became disseminated and the relation of tribes, nationalities and nations to the races. He takes the reader on a journey through the animal kingdom to the world of man and introduces him to the beginnings of human history, in the course of which the laws of evolution that apply to the organic world have been replaced by the qualitatively new laws of social development.

In the final chapter Professor Nesturkh, in addition to his exposureof racism, touches on such important scientific problems as “Race and Language”, “Race and Mentality”. He adduces convincing evidence of the absence of any causal relation between the racial groups and language groups of mankind; he also shows that all modern races and nations are identical in their mental abilities. Stress is properly laid on the tremendous successes of communist construction in the U.S.S.R. and socialist construction of the People’s Democracies of Europe and Asia. The experience of these countries has completely destroyed the reactionary myth that mankind is divided into “higher” and “lower” races and shown that all peoples, irrespective of their racial make-up, are capable of developing genuinely progressive culture and science. The unscientific concept of racism is also refuted by the economic, political and cultural development of the young states in Asia, Africa and Latin America, recently liberated from the yoke of colonialism.

A Western reviewer Coon has this to say about the book:

Its bibliogarphy of 43 sources include only two non-Soviet works, one by Charles Darwin and the other by Marx and Engels. All of the photographs have been retouched, and none accredited to its proper source; many are easily recognizable.

The text is divided into four sections : Definition of the Races of
Mankind, Races and Origins of Man, The Origin of Races, and Races and Racism. In Section One, Nesturkh follows the threefold classification of ” great races ” devised by the aforementioned Cheboksarov in 1956: (1) Negroid or Afro-Asian, (2) Europeoid or Eurasian, and (3) Mongoloid or Asio- American. Under the first category he lumps Negroes, Pygmies, Bushmen, Negritos, Australian aborigines, Tasmanians, and Melanesians.

Genetics is studiously avoided, except once, apparently a slip. Classifications of race by blood groups are passed by in silence.

He uses the word mutation once (the previously mentioned slip) to explain the parallel evolution of the African and Australoid dwarfs, and in this I agree.

The last Section is on “racists” whom he blasts but does not name, and on “racism ” which he says can be explained very simply, as follows : “The theory of ‘ higher’ and ‘ lower 5 races, of the right of one race to dominate over another, justifies war between nations – it is the ideological mask concealing imperialistic politics” (p. 98).

Having explained “racism” he then tries to disprove it. This too is very simple. According to him, the ” racists ” claim that rich people are dolichocephalic and poor people mesocephalic or brachycephalic. But in Sweden the “bourgeois,” workers, and peasants all have cephalic indices of 77.0. So much for “racism.”

He disproves Aryanism by showing, like Boas, that language is acquired independently of racial features. As a final blow, he discredits intelligence tests. ” Bourgeois ” scientists, he says, believe in intelligence tests, while “genuine scientists, of course, display a sharply negative attitude toward them” (p. 102).

He ends with a pean of praise for the elysian treatment of minorities
in the U. S. S. R., overlooking the forced migrations of the Kalmucks and others, the recurrent waves of anti-Semitism, and the recent troubles with African students.

It is important for educated Americans to read this book, alongside some of our domestic books and articles on the same subject.

Carleton S. Coon Human Biology, Vol. 37, No. 1 (February, 1965), pp. 57-59

The era when the book was published (in the 1960s) the Soviet science was just coming out of the pseudoscientific theories of Lysenko, who was a leading figure in the biological sciences in Soviet Russian from 1940s-50s. After he became director of the Institute of Genetics within the USSR’s Academy of Sciences, he used this position of power along with his political connections to push for anti-Mendelian doctrines in Soviet science and education. Soviet scientists who refused to renounce genetics were dismissed from their posts and left destitute. Hundreds if not thousands of others were imprisoned. Several were sentenced to death as enemies of the state, including the botanist Nikolai Vavilov. Scientific dissent from Lysenko’s theories of environmentally acquired inheritance was formally outlawed in the Soviet Union in 1948. Though Lysenko remained at his post in the Institute of Genetics until 1965, his influence on Soviet agricultural practice had declined by the 1950s. [some text from his wikipage] So it is no wonder, that Nesturkh’s book makes scant references to the idea of genetics and is driven by a larger agenda of the ideology of the state. The state of Soviet biology never fully recovered from this setback. Meanwhile, mainly due to efforts of Sakhrov (I may be wrong here), the physical sciences could actually work mostly without much interference from the state ideology.

The book was translated from the Russian by George Hanna and was designed by Vladimir An. The book was first published by Foreign Languages Publishing House in 1964/1966 (as no date is printed on the book).

PDF | OCR | Cover | Bookmarked | 146 p.

Original scan by IA user. We cleaned, OCRed, Bookmarked, added the cover.

The Internet Archive link.







I. Racial Characteristics and Their Study 11

2. The Negroid Great Race 18

3. The Europeoid Great Race 23

4· The Mongoloid Great Race 25

5· Features Common to All Races 29


1. Fossil Men of the Modern Type 31

2. Neanderthal Man-the Ancestor of Modern Man 33

3. Earliest Man-the Ancestor of the Neanderthaler  36

4. The Anthropoids-the Ancestors of the Earliest Men 41

5. The Racial Peculiarities of Man and the Anthropoid Type of

Structure 46

6. The Main Features of the Structure of the Human Body: Band,

Foot, Brain 52


1. The Races of Mankind-the Result of Historical Development 57

2. Geographical and Social Isolation 59

3. Natural Selection 61

4. Intermarriage 63

5. The Formation of the Great Races 66

6. The Europeoid Great Race 69

7. The Negroid Great Race 75

8. The Mongoloid Great Race 89


1. The Essence of Racism  96

2. Race and Language 99

3· Race and Mentality 101

4· Equality of Races and Nations in the U.S.S.R 105

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Linear Algebra: Problems Book – Ikramov

In this post, we will see the book Linear Algebra: Problems Book by H. D. Ikramov. This is the associated problem book for the Linear Algebra by V. V. Voyevodin which we saw in the last post.

About the book:

The present book closely follows the structure of the book by V. Voyevodin with some insignificant deviations demanded by the particulars of the course of study. Thus, since the corresponding topic of the course of lectures is studied at the very end of the first term, seminar classes cannot keep up with the course and so the section devoted to metric spaces is included in Chapter 8.

It is a basic requirement that any problem book should contain a sufficient number of useful and comprehensive problems for seminar classes, home-assignments, tests and examinations. The author hopes that this requirement has been fulfilled. Moreover, he has attempted to supply the strongest students with a material for personal study, and to lead them to problems currently faced in computational algebra.

PDF | OCR | Bookmarked | 330 p.

All credits to the original uploader.

The Internet Archive link.


Front Cover 1 ,-7
Title Page 4 ,-72
Contents 6 ,-161
Preface 8 ,-197
CHAPTER 1 Linear Spaces 12 42
1.0. Terminology and General Notes 12 ,42
1.1. Definition of Linear Space 18 ,457
1.2. Linear Dependence 20 ,372
1.3. Spans. Rank of Vector Sets 23 ,75
1.4. Basis and Dimension of Space 27 ,-144
1.5. Sum and Intersection of Subspaces 30 ,281
CHAPTER 2 Euclidean and Unitary Spaces 34 45
2.0. Terminology .and General Notes 34 ,45
2.1. Definition of Euclidean Space 36 ,405
2.2. Orthogonality, Orthonormal Basis, Orthogonalization Procedure 39 ,238
2.3. Orthogonal Complement, Orthogonal Sums of Subspaces 42 ,202
2.4. Lengths, Angles, Distances 46 ,232
2.5. Unitary Spaces 49 ,392
CHAPTER 3 Determinants 53 -105
3.0. Terminology and General Notes 53 ,-105
3.1. Evaluation and the Simplest Properties of Determinants 57 ,389
3.2. Minors, Cofactors and the Laplace Theorem 64 ,297
3.3. Determinants and the Volume of a Parallelepiped in a Euclidean Space 70 ,291
3.4. Computing the Determinants by the Elimination Method 75 ,72
CHAPTER 4 Systems of Linear Equations 82 -298
4.0. Terminology and General Notes 82 ,130
4.1. The Rank of a Matrix 83 ,526
4.2. Planes in a Linear Space 87 ,438
4.3. Planes in a Euclidean Space 90 ,170
4.4. Homogeneous Systems of Linear Equations 93 ,382
4.5. Nonhomogeneous Systems of Linear Equations 100 ,143
CHAPTER 5 Linear Operators and Matrices 108 598
5.0. Terminology and General Notes 109 ,85
5.1. The Definition of a Linear Operator, the Image and Kernel of an Operator 113 ,212
5.2. Linear Operations over Operators 118 ,291
5.3. Multiplication of Operators 120 ,490
5.4. Operations over Matrices 125 ,-43
5.5. The Inverse of a Matrix 138 ,147
5.6. The Matrix of a Linear Operator, Transfer to Another Basis, Equivalent and Similar Matrices 147 ,-43
CHAPTER 6 Linear Operator Structure 153 -213
6.0. Terminology and General Notes 153 ,-213
6.1. Eigenvalues and Eigenvectors 154 ,127
6.2. The Characteristic Polynomial 157 ,287
6.3. Invariant Subspaces 162 ,415
6.4. Root Subspaces and the Jordan Form 167 ,245
CHAPTER 7 Unitary Space Operators 179 -229
7.0. Terminology and General Notes 179 ,-148
7.1. Conjugate Operator. Conjugate Matrix 183 ,-174
7.2. Normal Operators and Matrices 188 ,238
7.3. Unitary Operators and Matrices 192 ,150
7.4. Hermitian Operators and Matrices 197 ,-331
7.5. Positive-Semi definite and Positive-Definite Operators and Matrices 202 ,470
7.6. Singular Values and the Polar Representation 209 ,232
7.7. Hermitian Decomposition 214 ,441
7.8. Pseudosolutions and Pseudoinverse Operators 217 ,143
7.9. Quadratic Forms 222 ,88
CHAPTER 8 Metric Problems in Linear Space 228 -331
8.0. Terminology and General Notes 228 ,-49
8.1. Normed Linear Space 231 ,274
8.2. Norms of Operators and Matrices 236 ,-112
8.3. Matrix Norms and Systems of Linear Equations 240 ,611
8.4. Matrix Norms and Eigenvalues 245 ,343
Hints 254 ,-229
Answers and Solutions 267 ,-59
Index 325 ,-23

Posted in books, mathematics, mir books, mir publishers, problem books | Tagged , , , , , , , , , , , , , , , , , , , | 2 Comments

Linear Algebra – Voyevodin

In this post, we will see the book Linear Algebra by V. V. Voyevodin. The associated problem book by by H. D. Ikramov can be seen here.

About the book:

This textbook is a comprehensive united course in linear algebra and analytic geometry based on lectures read by the author for many years at various institutes to future specialists in computational mathematics.
It is intended mainly for those in whose education computational mathematics is to occupy a substantial place. Much of the instruction in this speciality is connected with the traditional mathematical courses. Nevertheless the interests of computational mathematics make it necessary to introduce large enough changes in both the methods of presentation of these courses and their content.

The book was translated from the Russian by Vladimir Shokurov and was first published by Mir Publishers in 1983.

PDF | OCR | Bookmarked | 393 p.

All credits to the original uploader.

The Internet Archive link.


Front Cover 1
Title Page 4
Contents 5
Preface 9

PART I Vector Spaces 11 396

CHAPTER 1 Sets, Elements, Operations 11 396

1. Sets and elements 12 107
2. Algebraic operation 14 104
3. lnverse operation 18 588
4. Equivalence relation 20 95
5. Directed line segments 22 41
6. Addition of directed line segments 25 452
7. Groups 28 540
8. Rings and fields 31 85
9. Multiplication of directed line segments by a number 35 531
10. Vector spaces 38 517
11. Finite sums and products 41 21
12. Approximate calculations 44 311

CHAPTER 2 The Structure of a Vector Space 45 329

13. Linear combinations and spans 46 225
14. Linear dependence 48 79
15. Equivalent systems of vectors 51 465
16. The basis 54 146
17. Simple examples of vector spaces 56 143
18. Vector spaces of directed line segments 57 299
19. The sum and intersection of subspaces 61 113
20. The direct sum of subspaces 64 403
21. Isomorphism of vector spaces 66 90
22. Linear dependence and systems of linear equations 70 324

CHAPTER 3 Measurements in Vector Space 75 452

23. Affine coordinate systems 75 452
24. Other coordinate systems 80 429
25. Some problems 82 317
26. Scalar product 89 310
27. Euclidean space 92 67
28. Orthogonality 95 128
29. Lengths, angles, distances 99 109
30. Inclined line, perpendicular, projection 102 577

CHAPTER 4 The Volume of a System of Vectors in Vector Space 110 44

31. Euclidean isomorphism 106 533
32. Unitary spaces 107 223
33. Linear dependence and orthonormal systems 108 213
34. Vector and triple scalar products 110 171
35. Volume and oriented volume of a system of vectors 115 9
36. Geometrical and algebraic properties of a volume 118 299
37. Algebraic properties of an oriented volume 122 0
38. Permutations 125 595
39. The existence of an oriented volume 126 95
40. Determinants 128 333
41. Linear dependence and determinants 133 27
42. Calculation of determinants 136 137

CHAPTER 5 The Straight Line and the Plane in Vector Space 137 104

43. The equations of a straight line and of a plane 137 104
44. Relative positions 142 220
45. The plane in vector space 146 164
46. The straight line and the hyperplane 149 229
47. The half space 154 230

CHAPTER 6 The Limit in Vector Space 161 146

49. Metric spaces 161 146
50. Complete spaces 163 359
51. Auxiliary inequalities 166 542
52. Normed spaces 168 53
53. Convergence in the norm and coordinate convergence 170 116
54. Completeness of normed spaces 173 76
55. The limit and computational processes 175 35

PART II Linear Operators 177 197

CHAPTER 7 Matrices and Linear Operators 177 400

56. Operators 177 400
57. The vector space of operators 181 115
58. The ring of operators 183 232
59. The group of nonsingular operators 185 248
60. The matrix of an operator 188 21
61. Operations on matriees 192 139
62. Matrices and determinants 196 449
63. Change of basis 199 72
64. Equivalent and similar matrices 202 345

CHAPTER 8 The Characteristic Polynomial 205 424

65. Eigenvalues and eigenvectors 205 424
66. The characteristic polynomial 208 271
67. The polynomial ring 210 238
68. The fundamental theorem of algebra 214 318
69. Consequences of the fundamental theorem 218 5

CHAPTER 9 The Structureof a Linear Operator 223 530

70. Invariant subspaees 223 530
71. The operator polynomial 225 384
72. The triangular form 228 211
73. A direct sum of operators 229 277
74. The Jordan canonical form 232 291
75. The adjoint operator 236 326
76. The normal operator 240 329
77. Unitary and Hermitian operators 243 546
78. Operators A*A and AA* 246 282
79. Decomposition of an arbitrary operator 249 169
80. Operators in the real space 251 304
81. Matrices of a special form 254 39

CHAPTER 10 Metric Properties of an Operator 257 454

82. The continuity and boundedness of an operator 257 454
83. The norm of an operator 259 23
84. Matrix norms of an operator 263 283
85. Operator equations 266 243
86. Pseudosolutions andthe pseudoinverse operator 268 412
87. Perturbation and nonsingularity of an operator 271 16
88. Stable solution of equations 275 276
89. Perturbation and eigenvalues 280 104

PART III Bilinear Forms 283 296

CHAPTER 11 Bilinear and Quadratic Forms 284 107

90. General properties of bilinearand quadratic forms 284 107
91. The matrices of bilinear and quadratic forms 290 359
92. Reduction to canonical form 296 331
93. Congruence and matrix decompositions 304 368
94. Symmetric bilinear forms 309 240
95. Second degree hypersurfaces 316 273
96. Second degree curves 321 109
97. Second degree surfaces 328 331

CHAPTER 12 Bilinear Metric Spaces 333 227

98. The Gram matrix and determinant 334 4
99. Nonsingular subspaces 340 248
100. Orthogonality in bases 344 509
101. Operators and bilinear forms 350 352
102. Bilinear metric Isomorphism 355 480

CHAPTER 13 Bilinear Forms in Computational Processes 358 213

103. Orthogonalization processes 358 213
104. Orthogonalizatio of a power sequence 363 322
105. Methods of conjugate directions 368 289
106. Main variants 374 71
107. Operator equations and pseudoduality 377 313
108. Bilinear forms in spectral problems 382 248

Conclusion 388 498

INDEX 390 336

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