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L. Mirsky, “An Introduction to Linear Algebra”

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter. "The straight-forward clarity of the writing is admirable."—American Mathematical Monthly. Bibliography.

Reviews

Summary: Rigorous Linear Algebra

Rating: 5

This book provides a rigorous formulation of linear algebra aimed at Mathematics majors. However, the presentation though completely rigorous is essentially elementary, so that is should be accessibe to just about everyone who wants to get more than a superficial algorithmic view of the subject. (E,g. most people know how to calculate determinants but not knowing the abstract definitioon, are not in a position to understand or derive simple properties of determinats that make their manipulation so simple and painless)

Some great strengths of the book: 1st: We have exercises distributed all through the exposition, and these serve to reinforce simple consequences of results and definitions. 2nd: Problems, numerous at the end of each chapter, ranging from simple to really challenging.

Topics covered that many such texts ignore include: Matrix Analysis, Quadratic, Bilinear and Hermitian forms, Matrix Groups, inequalities arising from matrcies. All these in addition to the standard presentations.

A great book, not too abstract, and not too concrete.

Summary: The best intermediate linear algebra book

Rating: 5

This is the best intermediate linear algebra book that I've in my personal library. I recomend this book to anybody who want to take this subjet seriously. This book is the start point for more advanced studies about linear algebra, but the book, by selft, is no a advanced text.

This is a classic text. Mirsky, was born on December 19 of 1918, are referred in the files of McTutor like a mathematician centered in three investigation areas:

(i) The theory of numbers, where has studied r-free numbers, i.e. numbers not divisible by the r th power of any integer. There is obtained analogues of Vinogradov's result on the representation of an odd integer ace the sum of three you prevail, the Goldbach conjecture on the representation of an even integer ace the sum of two prevails, and the twin prevails conjecture. (ii) to Linear algebra, where has wrote his famous text An introduction to line algebra (this one) (1955) and went on to publish 35 papers on the topic. In matter there is proved results on the existence of main with given eigenvalues and given diagonal elements. (iii) Combinatorics, where has developed you devise coming from Hall's theorem: -

Any person whose tendency is this beautiful and potent branch of the mathematics should have this text in its personal library, at least in what concerns to the classic theory.

Other more modern texts (and also very good as that of Shilov for example) they try to focus the Lineal Algebra in a form more abstract that Mirsky, but for the classic content, this it is my favorite one.

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2.5 out of 5 by Book123