Problems and solutions in introductory and advanced matrix calculus. 2nd edition. (English) Zbl 1351.15001
Hackensack, NJ: World Scientific (ISBN 978-981-3143-78-4/hbk; 978-981-3143-79-1/pbk). x, 555 p. (2017).
The first edition [Zbl 1116.15001] is enlarged. The book contains the following chapters: 1. Basic operations; 2. Linear equations; 3. Kronecker product; 4. Traces, determinants and hyperdeterminants; 5. Eigenvalues and eigenvectors; 6. Spectral theorem; 7. Commutators and anticommutators; 8. Decomposition of matrices; 9. Functions of matrices; 10. Cayley-Hamilton theorem; 11. Hadamard product; 12. Norms and scalar products; 13. Vec operator; 14. Nonnormal matrices; 15. Binary matrices; 16. Star product; 17. Unitary matrices; 18. Groups, Lie groups and matrices; 19. Lie algebras and matrices; 20. Braid group; 21. Graphs and matrices; 22. Hilbert spaces and mutually unbiased bases; 23. Linear differential equations; 24. Differentiation and matrices; 25. Integration and matrices.
Reviewer: Jorma K. Merikoski (Tampere)
MSC:
| 15-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra |
| 00A07 | Problem books |
| 15A06 | Linear equations (linear algebraic aspects) |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A23 | Factorization of matrices |
| 34A30 | Linear ordinary differential equations and systems |
| 15A69 | Multilinear algebra, tensor calculus |
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
| 15A63 | Quadratic and bilinear forms, inner products |
| 20Gxx | Linear algebraic groups and related topics |
| 17B45 | Lie algebras of linear algebraic groups |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
