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Linear Algebra Done Right 2nd Edition by Sheldon Axler ISBN 0387982582 9780387982588

Name: Linear Algebra Done Right 2nd Edition by Sheldon Axler ISBN 0387982582 9780387982588
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Authors:Sheldon Axler , Series:Mathematics [36] , Author sort:Axler, Sheldon , Languages:Languages:eng , Published:Published:Jan 2024 , Publisher:Springer

SKU: EB-24966 Category: eBook PDF Tags: Algebra, Done, Linear, Right 2nd, Sheldon Axler

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ISBN 10: 0387982582
ISBN 13: 978-0387982588
Author: Sheldon Axler

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents – without having defined determinants – a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

Linear Algebra Done Right 2nd Table of contents:

Chapter 1: Vector Spaces

1.1 Vector Spaces
1.2 Subspaces
1.3 Span and Linear Independence
1.4 Basis and Dimension
1.5 Coordinates and Isomorphisms
1.6 The Dual Space

Chapter 2: Linear Maps

2.1 Linear Maps
2.2 The Kernel and Image of a Linear Map
2.3 Isomorphisms
2.4 Matrix Representation of Linear Maps
2.5 Change of Basis

Chapter 3: Eigenvalues and Eigenvectors

3.1 Eigenvalues and Eigenvectors
3.2 Diagonalization
3.3 The Minimal Polynomial
3.4 The Cayley-Hamilton Theorem
3.5 Invariant Subspaces

Chapter 4: Inner Product Spaces

4.1 Inner Products and Norms
4.2 Orthogonality
4.3 Orthonormal Sets
4.4 The Gram-Schmidt Process
4.5 Orthogonal Projections
4.6 The Polar Decomposition

Chapter 5: Operators on Finite-Dimensional Vector Spaces

5.1 Linear Operators
5.2 The Spectral Theorem for Normal Operators
5.3 Unitary Operators
5.4 Symmetric Operators

Chapter 6: Diagonalization and Triangularization

6.1 Diagonalizable Operators
6.2 Jordan Form
6.3 Triangularizable Operators
6.4 Nilpotent Operators

Chapter 7: Canonical Forms

7.1 The Jordan Canonical Form
7.2 Invariant Subspaces and Generalized Eigenvectors
7.3 Rational Canonical Form
7.4 The Rational Canonical Form for a Matrix

Chapter 8: Determinants

8.1 The Determinant
8.2 Properties of Determinants
8.3 Cramer’s Rule
8.4 The Relationship between Determinants and Eigenvalues

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