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This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices. Furthermore, specialized topics such as spectral theorem, nonnormal matrices and mutually unbiased bases are included. Many of the problems are related to applications for group theory, Lie algebra theory, wavelets, graph theory and matrix-valued differential forms, benefitting physics and engineering students and researchers alike. It also branches out to problems with tensors and the hyperdeterminant. Computer algebra programs in Maxima and SymbolicC++ have also been provided.
Traces, Determinants and Hyperdeterminants
Eigenvalues and Eigenvectors
Commutators and Anticommutators
Decomposition of Matrices
Functions of Matrices
Norms and Scalar Products
Groups, Lie Groups and Matrices
Lie Algebras and Matrices
Graphs and Matrices
Hilbert Spaces and Mutually Unbiased Bases
Linear Differential Equations
Differentiation and Matrices
Integration and Matrices
Readership: Undergraduate and graduate students and researchers in mathematics, physics and engineering.
Each chapter starts with an introduction giving definitions and outlining techniques
Includes modern techniques in matrix calculus
Considers applications of matrix calculus in group theory and Lie algebra