Graduate Thesis Or Dissertation
 

A study of symmetric matrices and quadratic forms over fields of characteristic two

Public Deposited

Downloadable Content

Download PDF
https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/s4655k56m

Descriptions

Attribute NameValues
Creator
Abstract
  • This thesis has four main results. First we find a reduction form for symmetric matrices over fields of characteristic two. This result parallels the diagonalization theorem for symmetric matrices over fields of characteristic not two. Secondly we reduce our reduction form to a canonical form in perfect fields of characteristic two. For our next result we find the number of solutions of an arbitrary quadratic form over a finite field of characteristic two. This result parallels work done by Dickson in fields of characteristic not two. Finally we make use of our second and third results to find the number of m by t matrices X such that X'AX = B, where A and B are nonsingular symmetric matrices of orders m and t respectively. This final result parallels work done by Carlitz in fields of characteristic not two.
Resource Type
Date Available
Date Issued
Degree Level
Degree Name
Degree Field
Degree Grantor
Commencement Year
Advisor
Academic Affiliation
Non-Academic Affiliation
Subject
Rights Statement
Publisher
Peer Reviewed
Language
Digitization Specifications
  • File scanned at 300 ppi using Capture Perfect 3.0 on a Canon DR-9050C in PDF format. CVista PdfCompressor 5.0 was used for pdf compression and textual OCR.
Replaces

Relationships

Parents:

This work has no parents.

In Collection:

Items

Thumbnail Title Date Uploaded Visibility Actions
file details FurchaJohnA1966_Redacted.pdf 2017-08-16 Public Download