A note on commuting pairs of matrices |
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Authors: | Robert M Guralnick |
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Institution: | Department of Mathematics , University of Southern California , Los Angels, CA, 90089-1113 |
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Abstract: | We give a short proof of the Motzkin-Taussky result that the variety of commuting pairs of matrices is irreducible. An easy consequence of this is that any two generated commutative subalgebra of n×n matrices has dimension at most n. We also answer an old question of Gerstenhaber by showing that the set of commuting triples of n×n matrices is not irreducible for n≥32. |
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