# Description and Count of the Extended Symmetric Space of SO(3,p)

## Session Number

Project ID: MATH 4

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## Advisor(s)

Dr. Ellen Ziliak; Benedictine University

## Discipline

Mathematics

## Start Date

22-4-2020 11:30 AM

## End Date

22-4-2020 11:55 AM

## Abstract

Our goal is to investigate a Special Orthogonal group of 3 by 3 matrices modulo p, denoted SO(3,p). Such matrices can be used in a multitude of fields, such as physics, chemistry and computer science. We began by generalizing the notion of symmetry as it pertains to matrices. For this investigation, we will use an inner automorphism of order two which is defined as theta(X) = MXM^{-1}. For a specific involution matrix M, we provide a count and description of the elements of the Extended Symmetric Space of 3 by 3 matrices defined as R = {X in SO(3,p) | theta(X) = X^(-1)}.

## Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Description and Count of the Extended Symmetric Space of SO(3,p)

Our goal is to investigate a Special Orthogonal group of 3 by 3 matrices modulo p, denoted SO(3,p). Such matrices can be used in a multitude of fields, such as physics, chemistry and computer science. We began by generalizing the notion of symmetry as it pertains to matrices. For this investigation, we will use an inner automorphism of order two which is defined as theta(X) = MXM^{-1}. For a specific involution matrix M, we provide a count and description of the elements of the Extended Symmetric Space of 3 by 3 matrices defined as R = {X in SO(3,p) | theta(X) = X^(-1)}.