Involutory matrices, modulo m

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^α), without duplication, for each prime power modulus P^α. Using these results, formulas for the number of distinct involutory matrices (mod P^α) 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^α) is used to characterize such matrices. Involutory matrices (mod P^α) 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Polytechnic Institute

Year dc:date.issued

1969

Author dc:creator

• Amey, Dorothy Mae

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/71017

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/71017