Record Details
A study of symmetric matrices and quadratic forms over fields of characteristic two
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | A study of symmetric matrices and quadratic forms over fields of characteristic two |
| Names |
Furcha, John Arthur
(creator) Carlson, David (advisor) |
| Date Issued | 1965-04-29 (iso8601) |
| Note | Graduation date: 1966 |
| 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. |
| Genre | Thesis/Dissertation |
| Topic | Matrices |
| Identifier | http://hdl.handle.net/1957/47866 |
