矩陣空間的保持問題

內(nèi)容概要

《矩陣空間的保持問題(英文版)》介紹矩陣論的一個(gè)研究領(lǐng)域----保持問題。主要內(nèi)容包括最小秩保持、秩加性保持、秩等價(jià)保持、平方零保持、k-冪保持、k-冪等保持、矩陣(廣義)逆保持、對(duì)合保持、伴隨保持、乘積保持等。

書籍目錄

PrefaceNotationChapter 1  Introduction to preserver problems  1.1  Definitions  1.2  Typical categories of preserver problems  1.3  Techniques of Preserver Problems  1.4  OrganizationChapter 2  Preservers of the smallest nonzero rank  2.1  Additive rank-1 preservers between spaces of rectangular matrices  2.2  Additive rank-1 preservers between spaces of symmetric matrices  2.3  Additive rank-1 preservers between spaces of Hermitian matrices  2.4  Additive rank-1 preservers from a space of triangular matrices to a space of square matrices  2.5  Additive rank-2 preservers between spaces of alternate matrices  2.6  Invertible linear rank-1 preservers on spaces of trace zero matrices  2.7  Invertibility (characteristic polynomial,determinant) preservers  2.8  Remarks on Chapter 2Chapter 3  Additive rank-additivity preservers and applications  3.1  Additive rank-additivity preservers on spaces of rectangular matrices  3.2  Additive rank-additivity preservers on spaces of symmetric matrices  3.3  Additive rank-additivity preservers on spaces of Hermitian matrices  3.4  Additive rank-additivity preservers on spaces of alternate matrices  3.5  Applications of additive rank-additivity preservers  3.6  Remarks on Chapter 3Chapter 4  Additive preservers of rank equivalence and applications  4.1  Main results  4.2  Proofs of main results  4.3  Remarks on Chapter 4Chapter 5  Linear square-zero preservers on spaces of square matrices  5.1  Main results  5.2  Proofs of main results  5.3  Remarks on Chapter 5Chapter 6  Preservers of k-power/k-potent  6.1  Additive preservers of idempotence between spaces of square matrices  6.2  Injective additive preservers of idempotence on spaces of triangular matrices  6.3  Linear preservers of idempotence between spaces of symmetric matrices  6.4  Several problems related to k-power and k-potent preservers  6.5  Preservers of k-power  6.6  Preservers of k-potent matrices  6.7  Jordan homomorphisms between of rings of square matrices  6.8  Preservers of idempotent relation  6.9  Remarks on Chapter 6Chapter 7  Preservers of inverses of matrices  7.1  Linear inverse preservers between spaces of matrices  7.2  Additive inverse preservers between spaces of matrices  7.3  Remarks on Chapter 7Chapter 8  Preservers of generalized inverses of matrices  8.1  Additive preservers of M-P inverses of matrices over fields  8.2  Additive preservers of {1,2}-inverses of matrices over fields  8.3  Additive preservers of group inverses of matrices over fields  8.4  Strong linear preservers of Moore-Penrose inverses of matrices over the two-element Boolean algebra  8.5  Covariant operator pairs on M-P Inverses of matrices between real finite dimensional division algebras  8.6  Remarks on Chapter 8Chapter 9  Linear preservers of involutory matrices  9.1  Main results  9.2  Proofs of main results  9.3  Remarks on Chapter 9Chapter 10  Additive adjoint preservers  10.1  Main results  10.2  Proofs of main results  10.3  Remarks on Chapter 10Chapter 11  Preservers of multiplication  11.1  Homomorphisms from one general linear group to another  11.2  Homomorphisms from a multiplicative matrix semigroup to another  11.3  Automorphisms of multiplicative semigroups of upper triangular matrices  11.4  Remarks on Chapter 11Appendix A  Fitting decomposition of a matrixAppendix B  Canonical form of a rank-additive matrix pairAppendix C  Canonical form of a matrix tripleAppendix D  Adjoint matricesBibliographyIndex

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《矩陣空間的保持問題(英文版)》：One of the very active research areas in matrix theory is the study of preserver problems,including linear preserver problems,additive preserver problems and multiplicative preserver problems,which concern the classification of maps on matrices or operators that preserve certain special properties.

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