Given the prime power factorization of a positive integer m, a method for calculating the number of all distinct n x n - involutory matrices (mod m) is derived. This is done by first developing a method for the construction and enumeration of involutory matrices (mod P<sup>α</sup>), without duplication, for each prime power modulus P<sup>α</sup>. Using these results, formulas for the number of distinct involutory matrices (mod P<sup>α</sup>) of order n are given where p is an odd prime, p=2, α= 1 and α > 1.
The concept of a fixed group associated with an involutory matrix (mod P<sup>α</sup>) is used to characterize such matrices. Involutory matrices (mod P<sup>α</sup>) of order n are considered as linear transformations on a vector space of n-tuples to provide uncomplicated proofs for the basic results concerning involutory matrices over a finite field. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/71017 |
| Date | January 1969 |
| Creators | Amey, Dorothy Mae |
| Contributors | Mathematics |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Thesis, Text |
| Format | iii, 51 leaves., application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20273060 |
Page generated in 0.0021 seconds