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The aim of this book is to provide an introduction to current advances of preserver problems on matrices and present the basic methods of studying preserver problems. In order to ensure that the content is self-contained, we took some conclusions and their proofs from other books or papers, which will be convenient to the readers. It is also intended to offer a collection of references on preserver problems on matrices.
Preface
Notation
Chapter1 Introduction to preserver problems
Chapter2 Preservers of the smallest nonzero rank
Chapter3 Additive rank-additivity preservers and applications
Chapter4 Additive preservers of rank equivalence and applications
Chapter5 Linear square-zero preservers on spaces of square matrices
Chapter6 Preservers of k-power/k-potent
Chapter7 Preservers of inverses of matrices
Chapter8 Preservers of generalized inverses of matrices
Chapter9 Linear preservers of involutory matrices
Chapter10 Additive adjoint preservers
Chapter11 Preservers of multiplication
Appendix A Fitting decomposition of a matrix
Appendix B Canonical form of a rank-additive matrix pair
Appendix C Canonical form of a matrix triple
Appendix D Adjoint matrices
Bibliography
Index
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