Classical adjoint commuting and determinant preserving linear maps on Kronecker products of Hermitian matrices

Authors

Wai Leong Chooi
KiamHeong Kwa

Document Type

Article

Publication Date

5-1-2020

Abstract

Let psi :circle times(d)(i=1) H-ni -> circle times(d)(i=1) H-ni be a linear map on the Kronecker product of spaces of Hermitian matrices H-ni of size n(i) >= 3. (If d= 1, we identify circle times(d)(i=1) H-ni with H-ni.) We establish a condition under which psi (adj (circle times(d )(i=1)A(i))) = adj (psi(circle times(d )(i=1)A(i))) if and only if det (psi(circle times(d )(i=1)A(i))) = det (circle times(d )(i=1)A(i)) for all circle times(d )(i=1)A(i) is an element of circle times(d)(i=1) H-ni. Then for d is an element of {1,2}, we apply this fact to characterize maps psi : circle times(d)(i=1) H-ni -> circle times(d)(i=1) H-ni such that psi (adj (circle times(d )(i=1)A(i))) = adj (psi(circle times(d )(i=1)A(i))) with some mild conditions.

Keywords

Classical adjoint commuting, determinant preserving, Kronecker product, Hermitian matrix

Divisions

MathematicalSciences

Funders

None

Publication Title

Linear & Multilinear Algebra

Volume

68

Issue

5

Publisher

Taylor & Francis Ltd

Publisher Location

2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND