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008			190402s2019 si a ob 001 0 eng
010			_z 2019003179
040			_aWSPC _beng _cWSPC
020			_a9789811202520 _q(ebook)
020			_z9789811202513 _q(hbk.)
050	0	4	_aQA188 _b.S662 2019
082	0	4	_a512.9/434 _223
100	1		_aHardy, Yorick, _d1976- _920911
245	1	0	_aMatrix calculus, Kronecker product and tensor product _h[electronic resource] : _ba practical approach to linear algebra, multilinear algebra and tensor calculus with software implementations / _cYorick Hardy, Willi-Hans Steeb.
250			_a3rd ed.
260			_aSingapore : _bWorld Scientific Publishing Co. Pte Ltd., _c©2019.
300			_a1 online resource (388 p.) : _bill.
538			_aMode of access: World Wide Web.
538			_aSystem requirements: Adobe Acrobat Reader.
588			_aTitle from web page (viewed April 2, 2019).
500			_aPrevious edition: Matrix calculus and Kronecker product : a practical approach to linear and multilinear algebra / Willi-Hans Steeb, Yorick Hardy (2011).
504			_aIncludes bibliographical references and index.
505	0		_aMatrix 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		_aApplications. 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			_a"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."-- _cPublisher's website.
650		0	_aMatrices. _92259
650		0	_aKronecker products. _921293
655		0	_aElectronic books. _93294
700	1		_aSteeb, W.-H. _93337
700	1		_aSteeb, W.-H. _tMatrix calculus and Kronecker product. _921294
856	4	0	_uhttps://www.worldscientific.com/worldscibooks/10.1142/11338#t=toc _zAccess to full text is restricted to subscribers.
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