Matrix calculus and Kronecker product with applications and C++ programs /
The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This book provides a comprehensive introduction to the Kronecke...
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Main Authors: | |
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Corporate Authors: | |
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Published: |
World Scientific Pub. Co.,
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Publisher Address: | Singapore ; River Edge, N.J. : |
Publication Dates: | 1997. |
Literature type: | eBook |
Language: | English |
Subjects: | |
Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3572#t=toc |
Summary: |
The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This book provides a comprehensive introduction to the Kronecker product of matrices together with its software implementation in C++ using an object-oriented design. |
Carrier Form: | 1 online resource (xi,254pages) |
Bibliography: | Includes bibliographical references (pages 249-251) and index. |
ISBN: | 9789812819390 |
Index Number: | QA188 |
CLC: | O241.6-39 |
Contents: | 1. Matrix calculus. 1.1. Definitions and notation. 1.2. Trace and determinant. 1.3. Eigenvalue problem. 1.4. Projection matrices. 1.5. Fourier and Hadamard matrices. 1.6. Transformation of matrices. 1.7. Permutation matrices. 1.8. Vec operator. 1.9. Vector and matrix norms. 1.10. Sequences of vectors and matrices. 1.11. Groups. 1.12. Lie algebras. 1.13. Application in quantum theory -- 2. Kronecker product. 2.1. Definitions and notations. 2.2. Basic properties. 2.3. Matrix multiplication. 2.4. Permutation matrices. 2.5. Trace and determinant. 2.6. Eigenvalue problem. 2.7. Projection matrices. 2.8. Spectral representation. 2.9. Fourier and Hadamard matrices. 2.10. Direct sum. 2.11. Vec operator. 2.12. Groups. 2.13. Group representation theory. 2.14. Inversion of partitioned matrices -- 3. Applications. 3.1. Spin matrices. 3.2. One-dimensional Ising model. 3.3. Fermi systems. 3.4. Dimer problem. 3.5. Two-dimensional Ising model. 3.6. One-dimensional isotropic Heisenberg model. 3.7. Quantum groups. 3.8. Lax representation. 3.9. Signal processing -- 4. Tensor product. 4.1. Hilbert spaces. 4.2. Hilbert tensor products of Hilbert spaces. 4.3. Spin and statistics for the n-body problem. 4.4. Exciton-phonon systems. 4.5. Interpretation of quantum mechanics -- 5. C++ software implementation. 5.1. Abstract data type and C++. 5.2. The vector class. 5.3. The matrix class. 5.4. Header file vector class. 5.5. Header file matrix class. |