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 ad-
             vanced 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                                   9
                      3 Determinants and Traces                           12
                      4 Eigenvalues and Eigenvectors                      22
                      5 Commutators and Anticommutators                   36
                      6 Decomposition of Matrices                         40
                      7 Functions of Matrices                             46
                      8 Linear Differential Equations                      54
                      9 Kronecker Product                                 58
                      10 Norms and Scalar Products                        67
                      11 Groups and Matrices                              72
                      12 Lie Algebras and Matrices                        86
                      13 Graphs and Matrices                              92
                      14 Hadamard Product                                 94
                      15 Differentiation                                   96
                      16 Integration                                      97
                      17 Numerical Methods                                99
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