Linear transformations on symmetric matrices II |
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Authors: | GH Chan MH Lim |
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Institution: |
a Department of Mathematics, National University of Singapore, Singapore
b Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia |
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Abstract: | Let Tbe a linear mapping on the space of n× nsymmetric matrices over a field Fof characteristic not equal to two. We obtain the structure of Tfor the following cases:(i) Tpreserves matrices of rank less than three; (ii) Tpreserves nonzero matrices of rank less than K + 1 where Kis a fixed positive integer less than nand Fis algebraically closed; (iii) Tpreserves rank Kmatrices where Kis a fixed odd integer and Fis algebraically closed. |
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