Matrix calculus, Kronecker product and tensor product (Record no. 72813)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05077nmm a2200409 a 4500 |
| 001 - CONTROL NUMBER | |
| control field | 00011338 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220711214223.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 190402s2019 si a ob 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9789811202520 |
| -- | (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| -- | (hbk.) |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 512.9/434 |
| 100 1# - AUTHOR NAME | |
| Author | Hardy, Yorick, |
| 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 ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Singapore : |
| Publisher | World Scientific Publishing Co. Pte Ltd., |
| Year of publication | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (388 p.) : |
| 500 ## - GENERAL NOTE | |
| Remark 1 | Previous edition: Matrix calculus and Kronecker product : a practical approach to linear and multilinear algebra / Willi-Hans Steeb, Yorick Hardy (2011). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 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 | |
| Remark 2 | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | "Our self-contained volume provides an accessible introduction to linear and multilinear algebra as well as tensor calculus. Besides the standard techniques for linear algebra, multilinear algebra and tensor calculus, many advanced topics are included where emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, Hopf algebra, Yang-Baxter relations, computer graphics, fractals, quantum mechanics, quantum computing, entanglement, teleportation and partial trace. All these fields are covered comprehensively. The volume contains many detailed worked-out examples. Each chapter includes useful exercises and supplementary problems. In the last chapter, software implementations are provided for different concepts. The volume is well suited for pure and applied mathematicians as well as theoretical physicists and engineers. New topics added to the third edition are: mutually unbiased bases, Cayley transform, spectral theorem, nonnormal matrices, Gâteaux derivatives and matrices, trace and partial trace, spin coherent states, Clebsch-Gordan series, entanglement, hyperdeterminant, tensor eigenvalue problem, Carleman matrix and Bell matrix, tensor fields and Ricci tensors, and software implementations."-- |
| 700 1# - AUTHOR 2 | |
| Author 2 | Steeb, W.-H. |
| 700 1# - AUTHOR 2 | |
| Author 2 | Steeb, W.-H. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://www.worldscientific.com/worldscibooks/10.1142/11338#t=toc |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 588 ## - | |
| -- | Title from web page (viewed April 2, 2019). |
| 520 ## - SUMMARY, ETC. | |
| -- | Publisher's website. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Matrices. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Kronecker products. |
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