Duality of the matrix transpose and matrix conjugate inverse maps

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Archival Material/Manuscript

Publication Date

2022

Abstract

Choi (1973) established a duality between the inversion and ad- junction of bounded invertible Hilbert space operators, giving analo- gies between the similarity and congruence relations. We discuss Choi’s results in the finite-dimensional setting and show that a similar duality can be found between another pair of maps, the matrix transpose and the matrix conjugate-inverse maps.

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Disciplines

Mathematics

Keywords

Matrices; Hilbert space; Matrix inversion

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