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On Simultaneous Similarity Of D-Tuples Of Commuting Square Matrices, Corey Connelly
On Simultaneous Similarity Of D-Tuples Of Commuting Square Matrices, Corey Connelly
USF Tampa Graduate Theses and Dissertations
It has been shown by B. Shekhtman that when any d-tuple A of pairwise commuting N × N matrices with complex entries is cyclic, then A is simultaneously similar to the d-tuple of commuting N × N matrices B if and only if B is cyclic, and the sets of polynomials in d variables which annihilate A and B are equivalent.
This thesis offers a further generalization of this result, demonstrating the necessary and sufficient conditions for the simultaneous similarity of n-cyclic d-tuples of commuting square complex-valued matrices.