Graduation Year
2022
Document Type
Thesis
Degree
M.A.
Degree Name
Master of Arts (M.A.)
Degree Granting Department
Mathematics and Statistics
Major Professor
Sherwin Kouchekian, Ph.D.
Committee Member
Boris Shekhtman, Ph.D.
Committee Member
Ivan Rothstein, Ph.D.
Keywords
Cyclicity, Finite Dimensional Vector Space, Linear Algebra, Linear Operators
Abstract
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.
Scholar Commons Citation
Connelly, Corey, "On Simultaneous Similarity of d-tuples of Commuting Square Matrices" (2022). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/9324
