Publication Date


Document Type


First Advisor

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

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematics


Algebra; Matrices


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.


Includes bibliographical references.


ii, 19 pages




Northern Illinois University

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