Linear transformations on symmetric matrices that preserve commutativity |
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Authors: | GH Chan MH Lim |
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Institution: | Department of Mathematics National University of Singapore Singapore;Department of Mathematics University of Malaya Kuala Lumpur, Malaysia |
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Abstract: | It is shown that if a nonsingular linear transformation T on the space of n-square real symmetric matrices preserves the commutativity, where n ?3, then T(A) = λQAQt + Q(A)In for all symmetric matricesA, for some scalar λ, orthogonal matrix Q, and linear functional Q. |
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