Matrix Calculus, Kronecker Product and Tensor Product

A Practical Approach to Linear Algebra, Multilinear Algebra and Tensor Calculus with Software Implementations

Yorick Hardy, Willi-Hans Steeb

• Publisher: WSPC
• Year: 2019
• eBook ISBN: 9789811202537
• Edition: 3
• Topic: Mathematics
• Subtopic: Linear Algebra
• Index: Mathematics

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.

Contents:

• Matrix Calculus
• Kronecker Product
• Applications
• Tensor Product
• Software Implementations

Readership: Students, engineers, researchers, and scientists in mathematical physics, applied mathematics, algebra & number theory, and numerical analysis.Multilinear Algebra;Tensor Calculus;Kronecker Product;Tensor Product;Linear Algebra;Computer Algebra0 Key Features:

• Covers all the fields in science where the tensor product and Kronecker productplay an important role
• Contains a practical introduction to multilinear algebra with many applications
• Provides a large number of computer algebra implementations for this topic
• Each chapter also contains supplementary problems to challenge the reader
• Describes all the different applications of the Kronecker product and tensor productin mathematics, applied mathematics, physics and engineering

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Preface
• Contents
• Symbol Index
• 1. Matrix Calculus
• 2. Kronecker Product
• 3. Applications
• 4. Tensor Product
• 5. Software Implementations
• Bibliography
• Index