Simultaneous triangularization of a pair of matrices whose commutator has rank two |
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Authors: | Thomas J. Laffey |
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Affiliation: | Department of Mathematics University College Belfield, Dublin 4, Ireland |
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Abstract: | Let A,B be n×n matrices with entries in an algebraically closed field F of characteristic zero, and let C=AB?BA. It is shown that if C has rank two and AiBjCk is nilpotent for 0?i, j?n?1, 1?k?2, then A, B are simultaneously triangularizable over F. An example is given to show that this result is in some sense best possible. |
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