Date of Award:
5-1993
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
Jerry Ridenhour
Committee
Russell Thompson
Committee
Bob Gunderson
Abstract
We characterized the group of linear operators that preserve sign-nonsingular matrices over Mn(R). Then we extended these results to n show that a linear operator T that strongly preserves L-matrices over Mm,n(R) if and only if T preserves L-matrices and T is also one to one on m,n the set of cells. We also characterized the group of linear operators that strongly preserve L-matrices.
In addition, we characterized the group of linear operators that preserve super L- matrices, the subset of L-matrix. Also we investigated linear operators that preserve totally L-matrices, the subset of L-matrix.
Chapters 1 and 2 of this dissertation contain some material of the work done by other researchers on the linear preserver problems and the properties of sign-nonsingular matrices and L-matrix. Characterizations of linear operators in Chapters 3, 4, 5, and 6 of this dissertation are new.
Checksum
a6b8fae4447aa49cf1e260958a1911bc
Recommended Citation
Ye, Shumin, "Linear Operators that Preserve Qualitative Matrix Structures" (1993). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7144.
https://digitalcommons.usu.edu/etd/7144
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