Graduate Thesis Or Dissertation

 

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

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

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  • 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.
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  • 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.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2014-04-30T17:57:02Z (GMT) No. of bitstreams: 1 FurchaJohnA1966_Redacted.pdf: 696226 bytes, checksum: e855192e530f8851f968a0b56417e2f8 (MD5)
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