Problems in Linear Algebra – Proskuryakov

In this post we will see Problems in Linear Algebra by I. V. Proskuryakov.

problems-in-linear-algebra-porskuryakov

From the Preface:

In preparing this book of problems the author attempted firstly, to give a sufficient number of exercises for developing skills in the solution of typical problems (for example, the computing of determinants with numerical elements, the solution of systems of linear equations with numerical coefficients, and the like), secondly, to provide problems that will help to clarify basic concepts and their interrelations (for example, the connection between the properties of matrices and those of quadratic forms, on the one hand and those of linear transformations, on the other), thirdly to provide for a set of problems that might supplement the course of lectures and help to expand the mathematical horizon of the student (instances are the properties of the Pfaffian of the skew-symmetric determinant, the properties of associated matrices, and so on).

Compared with other problem book, this one has few new basic features. They include problems dealing with polynomial matrices (Sec. 13), linear transformations of affine and metric spaces (Secs. 18 and 19), and a supplement devoted to group rings, and fields. The problems of the supplement deal with the most elementary portions of the theory. Still and all, I think it can be used in pre-seminar discussions in the first and second years of study.

Starred numbers indicated problems that have been worked out or provided with hints. Solutions are given for a small number of problems.

The book was translated from the Russian by George Yankovsky and was first published by Mir Publishers in 1978.

Note: Though the file size is large (~ 26 M) the scan quality is really poor and is barely readable at times. 2-in-1 page scan with lot of warping. We tried to rectify this but were unable to do so. There is a weird colour hue (pink and blue) on many of the pages. If any one has access to a better copy please let us know.

All credits to original uploader.

You can get the book here.

Link updated 01 Feb 2017

Contents

Preface 5

Chapter I
DETERMINANTS
Sec. 1. Second and third-order determinants 9
Sec. 2. Permutations and substitutions 17
Sec. 3. Definition and elementary properties of determinants of any order 22
Sec. 4. Evaluating determinants with numerical elements 31
Sec. 5. Methods of computing determinants of the n th order 33
Sec. 6. Monirs, cofactors and the Laplace theorem 65
Sec. 7. Multiplication of determinants 74
Sec. 8. Miscellaneous problems 86

Chapter II
SYSTEMS OF LINEAR EQUATIONS

Sec. 9. Systems of equation solved by the Cramer rule 95
Sec. 10. The rank of a matrix. The linear dependence of vectors and linear forms 105
Sec. 11. Systems of linear equations 115

Chapter III
MATRICES AND QUADRATIC FORMS

Sec. 12. Operations involving matrices 131
Sec. 13. Polynomial matrices 155
Sec. 14. Similar matrices, characteristic and minimal polynomials. Jordan and diagonal forms of a matrix. Functions of matrices. 166
Sec. 15. Quadratic forms 182

Chapter IV
VECTOR SPACES AND THEIR LINEAR TRANSFORMATIONS

Sec. 16. Affine vector spaces 195
Sec. 17. Euclidean and unitary vector spaces 205
Sec. 18. Linear transformations of arbitrary vector spaces 220
Sec. 19. Linear transformations of Euclidean and unitary vector spaces 236
Sec. 20. Groups 251
Sec. 21. Rings and fields 265
Sec. 22. Modules 275
Sec. 23. Linear spaces and linear transformations (appendices to Secs. 10 and 16 to 19) 280
Sec. 24. Linear, bilinear, and quadratic functions and forms (appendix to Sec. 15) 284
Sec. 25. Affine (or point-vector) spaces 288
Sec. 26. Tensor algebra 295

ANSWERS

Chapter I. Determinants 312
Chapter II. Systems of linear equations 342
Chapter III. Matrices and quadratic forms 359
Chapter IV. Vector spaces and their linear transformations 397
Supplement 427

Index 449

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31 Responses to Problems in Linear Algebra – Proskuryakov

  1. mir_fan says:

    Even i had created a cleaned pdf from this but it is all warped and not useful. I guess it is camera photos and not scanned ones. Even i tried a shot of scanning using cameras but angle , lighting, reflections, quality etc are nearly impossible to get right. Flatbed scanners are slow but vastly superior – just a suggestion to people.

  2. Charanjit Singh says:

    Sir I have camera pictures of 2 books Elemetary Mathematics by Dorofeev,Potapov, Problems in Mathematics by Govarov,They are in 2 folders.I dont know how to make them in a single unit.If those folders are helpful I can send a copy of them. Thanks

  3. m95 says:

    many thanks for this post

  4. naeem says:

    Hello, Thank you to everybody who is working on preserving these books and this knowledge. This particular book (Problems in Linear Algebra) I have downloaded a few times but I can’t unzip it as it says that it encountered an unknown zip method. Anybody else have that issue? I am using WinRAR for the unzipping.

  5. tola says:

    hi admin! can u share new link? cuz i cant download it. thank in advance

  6. Anakot Kalathil Rajarajan says:

    Please put this book in some place accessible. Current link does not give the book but a lot of run around. Problems in Linear Algebra – Proskuryakov. Archive site is good.

  7. MathsMafia says:

    I got this book in a used book stall today. Was pleasantly surprised by seeing Mir book in that shop.

  8. Anakot Kalathil Rajarajan says:

    Good or bad the link for download has been hijacked. Is there any place where I can get the book? I had a hard bound copy of this book when I was a student and learnt a lot solving these problems. It is a shame I cannot locate this book.

  9. please re upload onto archive thank you

  10. Arun says:

    another book on the topic “Problems in Higher Algebra Faddeev” is located here – http://www.isinj.com/aime/Problems%20in%20Higher%20Algebra%20-%20Faddeev,%20Sominskii%20(MIR,1972).pdf

  11. Pingback: Problems in Linear Algebra – Proskuryakov | ybalja

  12. Reblogged this on ybalja and commented:
    From the Preface:

    In preparing this book of problems the author attempted firstly, to give a sufficient number of exercises for developing skills in the solution of typical problems (for example, the computing of determinants with numerical elements, the solution of systems of linear equations with numerical coefficients, and the like), secondly, to provide problems that will help to clarify basic concepts and their interrelations (for example, the connection between the properties of matrices and those of quadratic forms, on the one hand and those of linear transformations, on the other), thirdly to provide for a set of problems that might supplement the course of lectures and help to expand the mathematical horizon of the student (instances are the properties of the Pfaffian of the skew-symmetric determinant, the properties of associated matrices, and so on).

    Compared with other problem book, this one has few new basic features. They include problems dealing with polynomial matrices (Sec. 13), linear transformations of affine and metric spaces (Secs. 18 and 19), and a supplement devoted to group rings, and fields. The problems of the supplement deal with the most elementary portions of the theory. Still and all, I think it can be used in pre-seminar discussions in the first and second years of study.

    Starred numbers indicated problems that have been worked out or provided with hints. Solutions are given for a small number of problems.

    The book was translated from the Russian by George Yankovsky and was first published by Mir Publishers in 1978.

    Note: Though the file size is large (~ 26 M) the scan quality is really poor and is barely readable at times. 2-in-1 page scan with lot of warping. We tried to rectify this but were unable to do so. There is a weird colour hue (pink and blue) on many of the pages. If any one has access to a better copy please let us know.

    All credits to original uploader.

    You can get the book here.

    Password, if needed: mirtitles

    Contents

    Preface 5

    Chapter I
    DETERMINANTS
    Sec. 1. Second and third-order determinants 9
    Sec. 2. Permutations and substitutions 17
    Sec. 3. Definition and elementary properties of determinants of any order 22
    Sec. 4. Evaluating determinants with numerical elements 31
    Sec. 5. Methods of computing determinants of the n th order 33
    Sec. 6. Monirs, cofactors and the Laplace theorem 65
    Sec. 7. Multiplication of determinants 74
    Sec. 8. Miscellaneous problems 86

    Chapter II
    SYSTEMS OF LINEAR EQUATIONS

    Sec. 9. Systems of equation solved by the Cramer rule 95
    Sec. 10. The rank of a matrix. The linear dependence of vectors and linear forms 105
    Sec. 11. Systems of linear equations 115

    Chapter III
    MATRICES AND QUADRATIC FORMS

    Sec. 12. Operations involving matrices 131
    Sec. 13. Polynomial matrices 155
    Sec. 14. Similar matrices, characteristic and minimal polynomials. Jordan and diagonal forms of a matrix. Functions of matrices. 166
    Sec. 15. Quadratic forms 182

    Chapter IV
    VECTOR SPACES AND THEIR LINEAR TRANSFORMATIONS

    Sec. 16. Affine vector spaces 195
    Sec. 17. Euclidean and unitary vector spaces 205
    Sec. 18. Linear transformations of arbitrary vector spaces 220
    Sec. 19. Linear transformations of Euclidean and unitary vector spaces 236
    Sec. 20. Groups 251
    Sec. 21. Rings and fields 265
    Sec. 22. Modules 275
    Sec. 23. Linear spaces and linear transformations (appendices to Secs. 10 and 16 to 19) 280
    Sec. 24. Linear, bilinear, and quadratic functions and forms (appendix to Sec. 15) 284
    Sec. 25. Affine (or point-vector) spaces 288
    Sec. 26. Tensor algebra 295

    ANSWERS

    Chapter I. Determinants 312
    Chapter II. Systems of linear equations 342
    Chapter III. Matrices and quadratic forms 359
    Chapter IV. Vector spaces and their linear transformations 397
    Supplement 427

    Index 449

  13. victomant says:

    can anyone provide working link for this book?

  14. harsh says:

    the access is denied

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