Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

PDF

University of South Florida

2022

Cyclicity

Articles 1 - 1 of 1

Full-Text Articles in Entire DC Network

On Simultaneous Similarity Of D-Tuples Of Commuting Square Matrices, Corey Connelly Jun 2022

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.