Matrix calculus, Kronecker product, and tensor product : (Record no. 59951)

000 -LEADER
fixed length control field 03148cam a22002658i 4500
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 190123s2019 nju b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9789811202513 (HB)
041 ## - LANGUAGE CODE
Language code of text/sound track or separate title eng
080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER
Universal Decimal Classification number 512.643
Item number HAR
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name Hardy, Yorick,
240 10 - UNIFORM TITLE
Uniform title Matrix calculus and Kronecker product
245 10 - TITLE STATEMENT
Title Matrix calculus, Kronecker product, and tensor product :
Sub Title a practical approach to linear algebra, multilinear algebra, and tensor calculus, with software implementations /
250 ## - EDITION STATEMENT
Edition statement 3rd edition.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication Singapore
Name of publisher World Scientific
Year of publication 2019
300 ## - PHYSICAL DESCRIPTION
Number of Pages 373p.
500 ## - GENERAL NOTE
General note Previous edition: Matrix calculus and Kronecker product : a practical approach to linear and multilinear algebra / Willi-Hans Steeb, Yorick Hardy (2011).<br/>Yorick Hardy (University of the Witwatersrand, South Africa), Willi-Hans Steeb (University of Johannesburg, South Africa).
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 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.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Matrices.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Kronecker products.
690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN)
Topical term or geographic name as entry element Mathematics
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Steeb, W.-H.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type BOOKS
Holdings
Withdrawn status Lost status Damaged status Not for loan Current library Shelving location Full call number Accession Number Koha item type
        IMSc Library First Floor, Rack No:30 Shelf No:7 512.643 HAR 77366 BOOKS
The Institute of Mathematical Sciences, Chennai, India

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