Problems And Solutions In Introductory And Advanced Matrix Calculus (Second Edition)

by Yorick Hardy, Willi-hans Steeb

Overview

This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices. Furthermore, specialized topics such as spectral theorem, nonnormal matrices and mutually unbiased bases are included. Many of the problems are related to applications for group theory, Lie algebra theory, wavelets, graph theory and matrix-valued differential forms, benefitting physics and engineering students and researchers alike. It also branches out to problems with tensors and the hyperdeterminant. Computer algebra programs in Maxima and SymbolicC++ have also been provided.

Product Details

ISBN-13:	9789813143791
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	09/06/2016
Pages:	568
Product dimensions:	6.70(w) x 9.60(h) x 1.20(d)

Table of Contents

Preface v

Notation ix

1 Basic Operations 1

2 Linear Equations 47

3 Kronecker Product 71

4 Traces, Determinants and Hyperdeterminants 99

5 Eigenvalues and Eigenvectors 142

6 Spectral Theorem 205

7 Commutators and Anticommutators 217

8 Decomposition of Matrices 241

9 Functions of Matrices 260

10 Cayley-Hamilton Theorem 299

11 Hadamard Product 309

12 Norms and Scalar Products 318

13 Vec Operator 340

14 Nonnormal Matrices 355

15 Binary Matrices 365

16 Star Product 371

17 Unitary Matrices 377

18 Groups, Lie Groups and Matrices 398

19 Lie Algebras and Matrices 439

20 Braid Group 466

21 Graphs and Matrices 486

22 Hilbert Spaces and Mutually Unbiased Bases 496

23 Linear Differential Equations 507

24 Differentiation and Matrices 520

25 Integration and Matrices 535

Bibliography 547

Index 551