Previous edition: Matrix calculus and Kronecker product : a practical approach to linear and multilinear algebra / Willi-Hans Steeb, Yorick Hardy (2011).
Yorick Hardy (University of the Witwatersrand, South Africa), Willi-Hans Steeb (University of Johannesburg, South Africa).

Includes bibliographical references and index.

Matrix calculus. Denitions and notation -- Matrix operations -- Gram-Schmidt orthonormalization -- Linear equations -- Mutually unbiased bases -- Trace and determinant -- Eigenvalue problem -- Cayley-Hamilton theorem -- Projection matrices -- Unitary, Fourier, and Hadamard matrices -- Transformation of matrices -- Cayley transform -- Permutation matrices -- Spectral theorem -- Singular value decomposition -- Pseudo inverse -- Vec operator -- Vector and matrix norms -- Sequences of vectors and matrices -- Commutators and anti-commutators -- Groups and Lie groups -- Lie algebras -- Functions of matrices -- Nonnormal matrices -- Kronecker product. Denitions and notations -- Basic properties -- Matrix multiplication -- Permutation matrices -- Trace and determinant -- Eigenvalue problem -- Projection matrices -- Unitary, Fourier, and Hadamard matrices -- Direct sum -- Kronecker sum -- Matrix decompositions -- Vec operator and Sylvester equation -- Groups -- Group representation theory -- Commutators and anti-commutators -- Inversion of partitioned matrices -- Nearest Kronecker product -- Gateaux derivative and matrices.

Applications. Trace and partial trace -- Pauli spin matrices -- Spin coherent states -- Pauli group, Cliord groups, and Bell group -- Applications in quantum theory -- Partition functions and thermodynamics -- Dimensional ising model -- Fermi systems -- Dimer problem -- Dimensional Ising model -- Dimensional Heisenberg model -- Hopf algebras -- Quantum groups -- Lax representation -- Signal processing -- Clebsch-gordan series -- Braid-like relations and yang-baxter relations -- Fast Fourier transform -- Entanglement -- Hyperdeterminant -- Tensor eigenvalue problem -- Carleman matrix and bell matrix -- Tensor product>> -- Hilbert spaces -- Hilbert tensor products of Hilbert spaces -- Spin and statistics for the n-body problem -- Exciton-phonon systems -- Interpretation of quantum mechanics -- Universal enveloping algebra -- Tensor fields, metric tensor fields, and ricci tensors -- Software implementations.