Hypermatrices are defined. Elementary operations and properties are defined and discussed. A 4-ary Multiplication is defined for hypermatrices, consisting of multilinear mappings from ordered 4-tuples of hypermatrices to hypermatrices. This multiplication is the only such mapping satisfying two basic properties which we should like such an operation to have. Various properties and characterizations of Multiplication are discussed.
Equivalence Classes of hypermatrices are defined and discussed. Starting with equivalence classes of a general nature, we are led to the definition of various types of Hyperdeterminants, themselves considered as being equivalence classes of hypermatrices. Operators and operations on hypermatrices are extended to hyperdeterminants. A generalization of the Cauchy-Binet Theorem for matrices is seen to hold for hypermatrices and their associated hyperdeterminants.
Special systems of hypermatrices are seen to constitute generalizations of the Complex and Quaternion Algebras, and some properties of these are discussed. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/39528 |
| Date | January 1961 |
| Creators | Delkin, Jay Ladd |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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