Article ID Journal Published Year Pages File Type
4598674 Linear Algebra and its Applications 2016 18 Pages PDF
Abstract

Maps that preserve adjacency on the set of all invertible hermitian matrices over a finite field are characterized. It is shown that such maps form a group that is generated by the maps A↦PAP⁎A↦PAP⁎, A↦AσA↦Aσ, and A↦A−1A↦A−1, where P   is an invertible matrix, P⁎P⁎ is its conjugate transpose, and σ is an automorphism of the underlying field. Bijectivity of maps is not an assumption but a conclusion. Moreover, adjacency is assumed to be preserved in one direction only.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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