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                                  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
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