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**About this book :- **
**Linear Algebra Done Right (2E) ** written by
** Sheldon Axler, Sheldon Jay **

The audacious title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue. Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must define determinants, prove that a linear map is not invertible if and only if its determinant equals 0, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues must exist.

In contrast, the simple determinant-free proofs presented here offer more insight. Once determinants have been banished to the end of the book, a new route opens to the main goal of linear algebra understanding the structure of linear operators. This book starts at the beginning of the subject, with no prerequisites other than the usual demand for suitable mathematical maturity. Even if your students have already seen some of the material in the first few chapters, they may be unaccustomed to working exercises of the type presented here, most of which require an understanding of proofs.

(Sheldon Axler)

**Book Detail :- **
** Title: ** Linear Algebra Done Right
** Edition: ** 2nd
** Author(s): ** Sheldon Axler, Sheldon Jay
** Publisher: ** Springer
** Series: ** Lecture Notes in Statistics
** Year: ** 1997
** Pages: ** 260
** Type: ** PDF
** Language: ** English
** ISBN: ** 0387982590,9780387982595
** Country: ** US

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**About Author :- **

Author ** Sheldon Axler ** was valedictorian of his high school in Miami, Florida. He received his AB from Princeton University with highest honors, followed by a PhD in Mathematics from the University of California at Berkeley. As a Moore Instructor at MIT, Axler received a university-wide teaching award.

Axler was then an assistant professor, associate professor, and professor in the Mathematics Department at Michigan State University, where he received the first J. Sutherland Frame Teaching Award and the Distinguished Faculty Award.

Axler received the Lester R. Ford Award for expository writing from the Mathematical Association of America in 1996. In addition to publishing numerous research papers, Axler is the author of five mathematics textbooks, ranging from freshman to graduate level. His book Linear Algebra Done Right has been adopted as a textbook at over 260 universities.

Axler has served as Editor-in-Chief of the Mathematical Intelligencer and as Associate Editor of the American Mathematical Monthly. He has been a member of the Council of the American Mathematical Society and a member of the Board of Trustees of the Mathematical Sciences Research Institute. Axler currently serves on the editorial board of Springer’s series Undergraduate Texts in Mathematics, Graduate Texts in Mathematics, and Universitext.

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**Book Contents :- **
**Linear Algebra Done Right (2E) ** written by
** Sheldon Axler, Sheldon Jay **
cover the following topics.

Preface for the Instructor

Preface for the Student

Acknowledgments

1. Vector Spaces

1.A Rn and Cn

1.B Definition of Vector Space

1.C Subspaces

2. Finite-Dimensional Vector Spaces

2.A Span and Linear Independence

2.B Bases

2.C Dimension

3. Linear Maps

3.A The Vector Space of Linear Maps

3.B Null Spaces and Ranges

3.C Matrices

3.D Invertibility and Isomorphic Vector Spaces

3.E Products and Quotients of Vector Spaces

3.F Duality

4. Polynomials

5. Eigenvalues, Eigenvectors, and Invariant Subspaces

5.A Invariant Subspaces

5.B Eigenvectors and Upper-Triangular Matrices

5.C Eigenspaces and Diagonal Matrices

6. Inner Product Spaces

6.A Inner Products and Norms

6.B Orthonormal Bases

6.C Orthogonal Complements and Minimization Problems

7. Operators on Inner Product Spaces

7.A Self-Adjoint and Normal Operators

7.B The Spectral Theorem

7.C Positive Operators and Isometries

7.D Polar Decomposition and Singular Value Decomposition

8. Operators on Complex Vector Spaces

8.A Generalized Eigenvectors and Nilpotent Operators

8.B Decomposition of an Operator

8.C Characteristic and Minimal Polynomials

8.D Jordan Form

9. Operators on Real Vector Spaces

9.A Complexification

9.B Operators on Real Inner Product Spaces

10. Trace and Determinant

10.A Trace

10.B Determinant

Photo Credits

Symbol Index

Index

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