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

Rusell Thompson

Committee

Bob Gunderson

Abstract

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.

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a6b8fae4447aa49cf1e260958a1911bc

Included in

Mathematics Commons

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