Linear transformations on matrices: The invariance of commuting pairs of matrices |
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Authors: | Leroy B. Beasley |
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Affiliation: | a Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada |
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Abstract: | Let L be a linear transformation on the set of all n×n matrices over an algebraically closed field of characteristic 0. It is shown that if AB=BA implies L(A)L(B)=L(B)L(A) and if either L is nonsingular or the implication in the hypothesis can also be reversed, then L is a sum of a scalar multiple of a similarity transformation and a linear functional times the identity transformation. |
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