#### Publication Date

1965

#### Document Type

Dissertation/Thesis

#### First Advisor

Christiano, John G.||Beach, James W.

#### Degree Name

M.S. (Master of Science)

#### Legacy Department

Department of Mathematics

#### LCSH

Algebra; Matrices

#### Abstract

The problem lies in finding the structure of a set of matrix transformations that operate on a set S of 6 x 6 matrices, with 6 elements, giving matrices that are in the set S. Each of the matrices in the set S, possess a common symmetry which facilitates a simple notation. There are only four distinct rows of elements for all the matrices in the set, S. Therefore, the matrices are noted by listing the type of rows found in the matrix. The transformations are written as permutations on 6 symbols. It was found that the structure of the set of transformations was based on finding two particular groups of order 6. The Cartesian product of these groups generated this set of transformations. On finding products of transformations of these two groups whose factors were not members of the groups mentioned above, a set of transformations was produced that rotated submatrices of the matrices in 6. No conclusion was reached as to the properties of the rotation transformations as related to the set of transformations that were produced by Cartesian products. We suggest that this study might be an interesting extension of the work presented here.

#### Recommended Citation

Hertel, Donald A., "Matrix transformations that leave the symmetry of certain matrices invariant" (1965). *Graduate Research Theses & Dissertations*. 3910.

https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/3910

#### Extent

ii, 19 pages

#### Language

eng

#### Publisher

Northern Illinois University

#### Rights Statement

In Copyright

#### Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

#### Media Type

Text

## Comments

Includes bibliographical references.