Transposing a matrix by similarity operations |
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Authors: | Norman L Hills |
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Institution: | Department of Mathematics Michigan State University East Lansing, Michigan 48824 USA |
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Abstract: | A matrix T is said to co-transpose a square matrix A if T?1AT=A′ and T?1A′T=A. For every n?3 there exists a real n×n matrix which cannot be co-transposed by any matrix. However, it is shown that the following classes of real matrices can be co-transposed by a symmetric matrix of order two: 2×2 matrices, normal matrices, and matrices whose square is symmetric. |
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