Matrix calculus and Kronecker product
Subtitle: a practical approach to linear and multilinear algebra
By: Willi-Hans Steeb, Yorick Hardy
Contributors: Hardy, Yorick, 1976-
Edition: 2nd ed.
Publisher: World Scientific
Published: 2011
Place of publication: Singapore; Hackensack, N.J
Language: eng
Number of pages: 308
ISBN-13: 9789814335317
Subjects: Matrices; Kronecker products
Notes: Includes bibliographical references (p. 301-304) and index.
Table of contents: title: Machine generated contents note: -- 1.; title: Matrix Calculus -- -- 1.1.; title: Definitions and Notation -- -- 1.2.; title: Matrix Operations -- -- 1.3.; title: Linear Equations -- -- 1.4.; title: Trace and Determinant -- -- 1.5.; title: Eigenvalue Problem -- -- 1.6.; title: Cayley-Hamilton Theorem -- -- 1.7.; title: Projection Matrices -- -- 1.8.; title: Fourier and Hadamard Matrices -- -- 1.9.; title: Transformation of Matrices -- -- 1.10.; title: Permutation Matrices -- -- 1.11.; title: Matrix Decompositions -- -- 1.12.; title: Pseudo Inverse -- -- 1.13.; title: Vec Operator -- -- 1.14.; title: Vector and Matrix Norms -- -- 1.15.; title: Rank-k Approximations -- -- 1.16.; title: Sequences of Vectors and Matrices -- -- 1.17.; title: Gram-Schmidt Orthonormalization -- -- 1.18.; title: Groups -- -- 1.19.; title: Lie Algebras -- -- 1.20.; title: Commutators and Anti-Commutators -- -- 1.21.; title: Functions of Matrices -- -- 2.; title: Kronecker Product -- -- 2.1.; title: Definitions and Notations -- -- 2.2.; title: Basic Properties -- -- 2.3.; title: Matrix Multiplication -- -- 2.4.; title: Permutation Matrices -- -- 2.5.; title: Trace and Determinant -- -- 2.6.; title: Eigenvalue Problem -- -- 2.7.; title: Projection Matrices -- -- 2.8.; title: Fourier and Hadamard Matrices -- -- 2.9.; title: Direct Sum --; title: 2.10.; title: Kronecker Sum -- -- 2.11.; title: Matrix Decompositions -- -- 2.12.; title: Vec Operator -- -- 2.13.; title: Groups -- -- 2.14.; title: Group Representation Theory -- -- 2.15.; title: Commutators and Anti-Commutators -- -- 2.16.; title: Inversion of Partitioned Matrices -- -- 2.17.; title: Nearest Kronecker Product -- -- 3.; title: Applications -- -- 3.1.; title: Spin Matrices -- -- 3.2.; title: Pauli Group, Clifford Groups and Bell Group -- -- 3.3.; title: Application in Quantum Theory -- -- 3.4.; title: Thermodynamics -- -- 3.5.; title: One Dimensional Ising Model -- -- 3.6.; title: Fermi Systems -- -- 3.7.; title: Dimer Problem -- -- 3.8.; title: Two Dimensional Ising Model -- -- 3.9.; title: One Dimensional Heisenberg Model -- -- 3.10.; title: Hopf Algebras -- -- 3.11.; title: Quantum Groups -- -- 3.12.; title: Lax Representation -- -- 3.13.; title: Signal Processing -- -- 3.14.; title: Clebsch-Gordan Series -- -- 3.15.; title: Braid-like Relations -- -- 3.16.; title: Fast Fourier Transform -- -- 3.17.; title: Image Compression -- -- 4.; title: Tensor Product -- -- 4.1.; title: Hilbert Spaces -- -- 4.2.; title: Hilbert Tensor Products of Hilbert Spaces -- -- 4.3.; title: Spin and Statistics for the n-Body Problem -- -- 4.4.; title: Exciton-Phonon Systems -- -- 4.5.; title: Interpretation of Quantum Mechanics -- -- 4.6.; title: Universal Enveloping Algebra -- -- 5.; title: Computer Algebra Implementations.