عنوان

Matrix calculus, Kronecker product, and tensor product:

(Number (ISBN

9789811202513 (hardcover : alk. paper)

Number

6243

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Matrix calculus, Kronecker product, and tensor product:

General Material Designation

[electronic resources]

Other Title Information

a practical approach to linear algebra, multilinear algebra, and tensor calculus, with software implementations

First Statement of Responsibility

/ by Yorick Hardy, Willi-Hans Steeb.

Edition Statement

3rd edition.

Place of Publication, Distribution, etc.

New Jersey

Name of Publisher, Distributor, etc.

: World Scientific

Date of Publication, Distribution, etc.

, 2019.

Specific Material Designation and Extent of Item

xiv, 373 pages.

Text of Note

Previous edition: Matrix calculus and Kronecker product: a practical approach to linear and multilinear algebra / Willi-Hans Steeb, Yorick Hardy (2011).

Text of Note

Includes bibliographical references (pages 365-368) and index.

Text of 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.

Text of 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.

0

0

General Material Designation

Matrix calculus and Kronecker product

Entry Element

Matrices.

Entry Element

Kronecker products.

Subject Term

Calculus.

Edition

Entry Element

Hardy, Yorick, 1976- ,

Relator Code

Author

Entry Element

Steeb, Willi-Hans,

Entry Element

Steeb, W.-H.

Relator Code

Cllaborator

Country

ایران

Agency

Central Library of the Kurdistan University

Date of Transaction

20190201191648.0

Cataloguing Rules (Descriptive Conventions))

rda

e

BL

280328

a

Y