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.

Contents:

• Basic Operations
• Linear Equations
• Determinants and Traces
• Eigenvalues and Eigenvectors
• Commutators and Anticommutators
• Decomposition of Matrices
• Functions of Matrices
• Linear Differential Equations
• Kronecker Product
• Norms and Scalar Products
• Groups and Matrices
• Lie Algebras and Matrices
• Graphs and Matrices