Problems and Solutions in Matrix Calculus - University of Johannesburg

Problems and Solutions in Matrix Calculus

by Willi-Hans Steeb International School for Scientific Computing at University of Johannesburg, South Africa

Preface

The manuscript supplies a collection of problems in introductory and advanced matrix problems. Prescribed book: "Problems and Solutions in Introductory and Advanced Matrix Calculus", 2nd edition by Willi-Hans Steeb and Yorick Hardy World Scientific Publishing, Singapore 2016

v

Contents

Notation

x

1 Basic Operations

1

2 Linear Equations

13

3 Determinants and Traces

18

4 Eigenvalues and Eigenvectors

27

5 Commutators and Anticommutators

42

6 Decomposition of Matrices

46

7 Functions of Matrices

52

8 Linear Differential Equations

59

9 Kronecker Product

63

10 Norms and Scalar Products

71

11 Groups and Matrices

76

12 Lie Algebras and Matrices

87

13 Graphs and Matrices

93

14 Hadamard Product

95

15 Differentiation

97

16 Integration

98

17 Numerical Methods

100

vii

18 Miscellaneous

107

Bibliography

138

Index

141

viii

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download