Date of Award:
5-1991
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Mathematics and Statistics
Committee Chair(s)
LeRoy B. Beasley
Committee
LeRoy B. Beasley
Committee
Kathryn Turner
Committee
Larry Cannon
Committee
Duane Loveland
Committee
Bob Gunderson
Abstract
We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = Xr1 + Xr2 + ... + Xrt and r1>r2>...>rt≥2.
In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We also extended these results to linear operators that strongly preserve the matrix polynomial equation p(X) = I where p(X) is as above.
Chapters I and II of this thesis contain background material and summaries of the work done by other researchers on the linear preserver problem. Characterizations of linear operators in chapters III, IV, V, and VI of this thesis are new.
Checksum
9d44a5a1fc7d2cf555046b6d9b7f1cd8
Recommended Citation
Lee, Sang-Gu, "Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings" (1991). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 6984.
https://digitalcommons.usu.edu/etd/6984
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