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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.
Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle
Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle
Honors Theses
This senior project outlines potential lecture activities for a guest speaker or teacher in a high school classroom to present interesting applications of linear algebra. These applications are meant to be pertinent to things students at this age level are already learning or are interested in. The activities are designed such that the ideas of upper-level math are introduced in a very guided and non-intense way. The intent of the activities is mostly applications and interesting results rather than mathematical lecturing or instruction.
The high school level courses explored in this project are chemistry, economics, and health/physical education. For these …