Date of Award:
Doctor of Philosophy (PhD)
Mathematics and Statistics
LeRoy B. Beasley
We characterized the group of linear operators that preserve sign-nonsingular matrices over ��(ℝ). Then we extended these results to n show that a linear operator T that strongly preserves L-matrices over ��,�(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.
Ye, Shumin, "Linear Operators that Preserve Qualitative Matrix Structures" (1993). All Graduate Theses and Dissertations. 7144.
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .