## Problems in Linear Algebra – Proskuryakov

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

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.

You can get the book here.

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

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

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

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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### 35 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.

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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

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• The Mitr says:

This post can be useful. Otherwise you can upload the pictures in a zip file, somewhere we can get them. Hope this helps.

D

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• Stevin says:

Hello,

I have stumbled upon two MIR publisher books in pdf form, located through these links : Introductory Mathematics for Engineers by A.D. Myskis ( http://www.freelibros.com/ingenieria/introductory-mathematics-for-engineers-a-d-myskis.html ), and Mathematical Models of Electric Machines by Kopylov ( http://www.freelibros.com/electricidad/mathematical-models-of-electric-machines-i-p-kopylov.html ). I have obtained them through the depositfiles link. This is a Spanish website but the books are in English. If you would like me to send you the pdf files please let me know.

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• The Mitr says:

Thanks for the links. We already have a post for Mathematical Models of Electric Machines.

D

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• Shovon says:

Hi Steven,
I would be very grateful if you can help me with this one.
Introductory Mathematics for Engineers by A.D. Myskis

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• Shovon says:

It worked but not easily at all.
Thanks a lot.

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• The Mitr says:

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• Stevin says:

@Charanjit Singh, hello I’ve been eagerly searching for MIR books on elementary mathematics such as Elementary Mathematics Dorofeev. If you don’t have the time I could perform the process The Mitr recommended to you if you e-mail them to me. What do you think?

In general I’d like to say thank you very much to The Mitr, I’ve been following this website for quite some time and really appreciate all these books.

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3. m95 says:

many thanks for this post

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• Shovon says:

It worked but not that easily.
Thanks a lot.

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• Bóng Mưa says:

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• The Mitr says:

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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.

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5. tola says:

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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.

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• The Mitr says:

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7. MathsMafia says:

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

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• Chris yessayan says:

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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.

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• The Mitr says:

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• The Mitr says:

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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

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11. 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.

You can get the book here.

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

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

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

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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12. victomant says:

can anyone provide working link for this book?

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13. harsh says:

the access is denied

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14. Sidd says: