https://mklab.gr/ Wed, 29 Jul 2026 08:52:51 +0000 MyBB https://mklab.gr/showthread.php?tid=1150 Thu, 16 Jul 2026 04:29:41 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1150 Lecture notes for Math 115A (linear algebra)
by Terence Tao

Summary

This document contains Terence Tao’s comprehensive undergraduate lecture notes for Math 115A, an introductory course in linear algebra taught at UCLA in Fall 2002, which closely aligns with the Friedberg, Insel, and Spence textbook. Rather than focusing purely on computational mechanics, these notes emphasize the foundational theory, conceptual definitions, and rigorous mathematical proofs behind linear systems. 

The curriculum is systematically structured into a multi-week progression: the first two weeks establish the foundational rules of vector spaces, subspaces, linear independence, spans, bases, and dimensions; weeks three through five examine the algebraic properties of linear transformations and their coordinate representations; weeks six through eight shift the focus to matrix analysis, introducing tools such as determinants, eigenvectors, eigenvalues, trace, and diagonalization to simplify and visualize complex transformations; and the final weeks introduce inner product spaces, which extend vector spaces to include geometric concepts like lengths, angles, and orthogonality. Ultimately, Tao frames linear algebra as the study of linear transformations, illustrating how multidimensional systems can be elegantly decomposed and solved through systematic algebraic frameworks.


NOTES [PDF]]]> Lecture notes for Math 115A (linear algebra)
by Terence Tao

Summary

This document contains Terence Tao’s comprehensive undergraduate lecture notes for Math 115A, an introductory course in linear algebra taught at UCLA in Fall 2002, which closely aligns with the Friedberg, Insel, and Spence textbook. Rather than focusing purely on computational mechanics, these notes emphasize the foundational theory, conceptual definitions, and rigorous mathematical proofs behind linear systems. 

The curriculum is systematically structured into a multi-week progression: the first two weeks establish the foundational rules of vector spaces, subspaces, linear independence, spans, bases, and dimensions; weeks three through five examine the algebraic properties of linear transformations and their coordinate representations; weeks six through eight shift the focus to matrix analysis, introducing tools such as determinants, eigenvectors, eigenvalues, trace, and diagonalization to simplify and visualize complex transformations; and the final weeks introduce inner product spaces, which extend vector spaces to include geometric concepts like lengths, angles, and orthogonality. Ultimately, Tao frames linear algebra as the study of linear transformations, illustrating how multidimensional systems can be elegantly decomposed and solved through systematic algebraic frameworks.


NOTES [PDF]]]> https://mklab.gr/showthread.php?tid=343 Sun, 14 Jun 2026 15:43:43 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=343 Problems In Linear Algebra
by I. V. Proskuryakov

Summary 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.

BOOK PAGE]]> Problems In Linear Algebra
by I. V. Proskuryakov

Summary 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.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=342 Sun, 14 Jun 2026 15:41:20 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=342 Linear Algebra: Problems Book
by H. D. Ikramov

Summary 
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.

BOOK PAGE]]> Linear Algebra: Problems Book
by H. D. Ikramov

Summary 
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.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=269 Wed, 10 Jun 2026 22:43:01 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=269 Daivd Austin

Summary

"Understanding Linear Algebra" by Austin.  Introduces many applications so that readers appreciate how linear algebra plays a vital role in our society. Computer animation, image compression, Google PageRank, least squares, principal component analysis, and singular value decompositions. The book is used in over 100 institutions, from R1s to community colleges and high schools. 

BOOK PAGE]]> Daivd Austin

Summary

"Understanding Linear Algebra" by Austin.  Introduces many applications so that readers appreciate how linear algebra plays a vital role in our society. Computer animation, image compression, Google PageRank, least squares, principal component analysis, and singular value decompositions. The book is used in over 100 institutions, from R1s to community colleges and high schools. 

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=241 Wed, 10 Jun 2026 03:09:29 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=241 Elementary Linear Algebra
by Keith Matthews

Summary  This an introduction to linear algebra with solutions to all exercises. It covers linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations, and three–dimensional geometry.

BOOK PAGE]]> Elementary Linear Algebra
by Keith Matthews

Summary  This an introduction to linear algebra with solutions to all exercises. It covers linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations, and three–dimensional geometry.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=212 Wed, 10 Jun 2026 01:25:27 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=212 Vector Calculus
by Michael Corral

Summary  This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as "Vector Calculus", "Multivariable Calculus", or simply "Calculus III". The prerequisites are the standard courses in single-variable calculus (a.k.a. Calculus I and II).

BOOK PAGE]]> Vector Calculus
by Michael Corral

Summary  This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as "Vector Calculus", "Multivariable Calculus", or simply "Calculus III". The prerequisites are the standard courses in single-variable calculus (a.k.a. Calculus I and II).

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=200 Wed, 10 Jun 2026 00:29:42 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=200 Linear Algebra: A Course for Physicists and Engineers
by Arak Mathai,‎ Hans J. Haubold

Summary  In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered.

BOOK PAGE]]> Linear Algebra: A Course for Physicists and Engineers
by Arak Mathai,‎ Hans J. Haubold

Summary  In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=152 Mon, 08 Jun 2026 19:58:34 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=152 Linear Algebra Done Right

Sheldon Axler

Summary :  This best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.

BOOK PAGE

]]> Linear Algebra Done Right

Sheldon Axler

Summary :  This best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.

BOOK PAGE

]]> https://mklab.gr/showthread.php?tid=151 Mon, 08 Jun 2026 19:55:37 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=151 Interactive Linear Algebra 
Dan Margalit

Interactive Linear Algebra by Dan Margalit and Joseph Rabinoff is an open-source textbook that bridges the gap between algebraic calculations and geometric intuition. It emphasizes that computers handle raw calculations best, focusing instead on developing a conceptual framework and visual understanding of matrix operations

BOOK PAGE]]> Interactive Linear Algebra 
Dan Margalit

Interactive Linear Algebra by Dan Margalit and Joseph Rabinoff is an open-source textbook that bridges the gap between algebraic calculations and geometric intuition. It emphasizes that computers handle raw calculations best, focusing instead on developing a conceptual framework and visual understanding of matrix operations

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=150 Mon, 08 Jun 2026 19:53:13 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=150 Linear Algebra Done Wrong 
Sergei Treil

Summary : It is supposed to be a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous mathematics that is presented in a "cookbook style" calculus type course.

BOOK PAGE]]> Linear Algebra Done Wrong 
Sergei Treil

Summary : It is supposed to be a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous mathematics that is presented in a "cookbook style" calculus type course.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=149 Mon, 08 Jun 2026 19:50:06 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=149 Introduction to Applied Linear Algebra
Stephen Boyd

Introduction to Applied Linear Algebra by Stephen Boyd and Lieven Vandenberghe is a practical, application-driven textbook that teaches essential mathematical concepts for engineering, data science, and AI. It skips abstract proofs to focus heavily on vectors, matrices, and least squares modeling, demonstrating how linear algebra drives real-world technology.

BOOK PAGE]]> Introduction to Applied Linear Algebra
Stephen Boyd

Introduction to Applied Linear Algebra by Stephen Boyd and Lieven Vandenberghe is a practical, application-driven textbook that teaches essential mathematical concepts for engineering, data science, and AI. It skips abstract proofs to focus heavily on vectors, matrices, and least squares modeling, demonstrating how linear algebra drives real-world technology.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=148 Mon, 08 Jun 2026 19:47:24 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=148 Introduction to vectors and tensors 
Ray M Bowen

Summary :  This work represents our effort to present the basic concepts of vector and tensor analysis. Volume I begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume II begins with a discussion of Euclidean Manifolds which leads to a development of the analytical and geometrical aspects of vector and tensor fields. a discussion of general differentiable manifolds.

VOLUME 1

VOLUME 2]]> Introduction to vectors and tensors 
Ray M Bowen

Summary :  This work represents our effort to present the basic concepts of vector and tensor analysis. Volume I begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume II begins with a discussion of Euclidean Manifolds which leads to a development of the analytical and geometrical aspects of vector and tensor fields. a discussion of general differentiable manifolds.

VOLUME 1

VOLUME 2]]> https://mklab.gr/showthread.php?tid=147 Mon, 08 Jun 2026 19:42:46 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=147 Linear Algebra 
David Cherney

This "textbook" (+videos+WeBWorKs) is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.

BOOK PAGE]]> Linear Algebra 
David Cherney

This "textbook" (+videos+WeBWorKs) is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=146 Mon, 08 Jun 2026 19:40:45 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=146 A First Courses in Linear Algebra 
Rob Breezer

"A First Course in Linear Algebra" by Robert A. Beezer is a highly regarded, open-source textbook. It bridges matrix algebra and abstract vector spaces while teaching formal mathematical techniques like proof writing. The text features fully worked examples, complete proofs, and interactive Sage integration

BOOK PAGE]]> A First Courses in Linear Algebra 
Rob Breezer

"A First Course in Linear Algebra" by Robert A. Beezer is a highly regarded, open-source textbook. It bridges matrix algebra and abstract vector spaces while teaching formal mathematical techniques like proof writing. The text features fully worked examples, complete proofs, and interactive Sage integration

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=145 Mon, 08 Jun 2026 19:38:26 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=145 Elementary Linear Algebra 
Keith Matthews

"Elementary Linear Algebra" by Keith Matthews (University of Queensland), originally written as lecture notes in 1991 and hosted on the Number Theory Web.
Unlike the more abstract and coordinate-free approaches seen in advanced algebra texts, this book is a highly direct, computationally grounded introduction. It focuses heavily on exact arithmetic and matrix calculations over the fields of rational, real, and complex numbers.

BOOK PAGE]]> Elementary Linear Algebra 
Keith Matthews

"Elementary Linear Algebra" by Keith Matthews (University of Queensland), originally written as lecture notes in 1991 and hosted on the Number Theory Web.
Unlike the more abstract and coordinate-free approaches seen in advanced algebra texts, this book is a highly direct, computationally grounded introduction. It focuses heavily on exact arithmetic and matrix calculations over the fields of rational, real, and complex numbers.

BOOK PAGE]]>