#### 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

#### Recommended Citation

Salazar, Tomas Eufracio. "An Abstract Matrix Model: The Column Model." (1976). https://digitalrepository.unm.edu/math_etds/136