Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/70494 |
| Date | January 1967 |
| Creators | Chesley, Daniel Sprigg |
| Contributors | Mathematics |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 36 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20395114 |
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