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 Matrics
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

As an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students. The coverage includes systems of linear equations, linear differential equations, functions of matrices and the Kronecker product. Many of the problems are related to applications in areas such as group theory, Lie algebra theory and graph theory. Thus, physics and engineering students will also benefit from the book. Exercises for matrix-valued differential forms are also included. ---summary provided by publisher