Publication Date

7-21-1976

Abstract

In this dissertation we introduce an abstract model for matrix theory, The Column Model. We investigate some properties of the special class of partially ordered linear algebras that satisfy the conditions of the Model. We use the order structure of the Model to obtain some results on: idempotents in the Model, nonnegative elements of the Model having nonnegative generalized inverses, factor theorems in the Model and concepts in the Model that are related to the usual notion of eigenvalues of an m-by-m matrix. Since the set of m-by-m matrices belongs to the special class of partially ordered linear algebras satisfying the conditions of the Model, the results obtained hold for the set of m-by-m matrices.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Ralph Elgin DeMarr

Second Committee Member

Steven Arthur Pruess

Third Committee Member

Arthur Steger

Language

English

Document Type

Dissertation

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