descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1976 English Publisher:Canadian Mathematical SocietyJournal:Canadian Journal of Mathematics, volume 28, pages 455-472 (issn: 0008-414X, eissn: 1496-4279,

Authors: Ong, Hock; Botta, E. P.;

doi: 10.4153/cjm-1976-047-9

Linear Transformations On Matrices: The Invariance of Generalized Permutation Matrices, I

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Abstract

Let F be a field, Mn(F) be the vector space of all w-square matrices with entries in F and a subset of Mn(F). It is of interest to determine the structure of linear maps T : Mn(F) →Mn(F) such that . For example: Let be GL(n, C), the group of all nonsingular n X n matrices over C [5]; the subset of all rank 1 matrices in MmXn(F) [4] (MmXn(F) is the vector space of all m X n matrices over F) ; the unitary group [2] ; or the set of all matrices X in Mn(F) such that det(X) = 0 [1]. Other results in this direction can be found in [3].

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University of Toronto
Canada

Keywords

Vector and tensor algebra, theory of invariants

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