A Second Course in Linear Algebra Cambridge Mathematical Textbooks 1st Edition by Stephan Ramon Garcia,Roger A Horn ISBN 1107103819 9781107103818

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Product details:

ISBN 10: 1107103819 

ISBN 13: 9781107103818

Author: Stephan Ramon Garcia, Roger A. Horn

Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. Concise chapters promote a focused progression through essential ideas, and contain many examples and illustrative graphics. In addition, each chapter contains a bullet list summarising important concepts, and the book includes over 600 exercises to aid the reader’s understanding. Topics are derived and discussed in detail, including the singular value decomposition, the Jordan canonical form, the spectral theorem, the QR factorization, normal matrices, Hermitian matrices (of interest to physics students), and positive definite matrices (of interest to statistics students).

Table of contents: 

Preface

Notation

0. Preliminaries

1. Vector Spaces

2. Bases and Similarity

3. Block Matrices

4. Inner Product Spaces

5. Orthonormal Vectors

6. Unitary Matrices

7. Orthogonal Complements and Orthogonal Projections

8. Eigenvalues, Eigenvectors, and Geometric Multiplicity

9. The Characteristic Polynomial and Algebraic Multiplicity

10. Unitary Triangularization and Block Diagonalization

11. Jordan Canonical Form

12. Normal Matrices and the Spectral Theorem

13. Positive Semidefinite Matrices

14. The Singular Value and Polar Decompositions

15. Singular Values and the Spectral Norm

16. Interlacing and Inertia

Appendix A: Complex Numbers

References

Index

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