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.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8244 |
| Date | 01 May 1993 |
| Creators | Ye, Shumin |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
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