Finite-Dimensional Ternary Algebras

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Abstract:

A ternary algebra is a linear space Alpha over the complex numbers such that for any three elements A, B and C in Alpha there exists a product AB*C in Alpha satisfying certain axioms which reduce to ordinary properties of matrix multiplication when the elements of Alpha are matrices and * denotes conjugate transpose. The present paper is devoted to a study of the algebraic structure of ternary algebras. In particular it is shown that an arbitrary finite-dimensional ternary algebra has a representation as a ternary algebra of matrices.

Author(s):
Ritea, Howard B.
Author Organization(s):
CALIFORNIA UNIV LOS ANGELES
Funding Organization(s):
Office of Naval Research, Washington , DC
Document Type:
Technical Report/Doctoral Thesis
Publication Date:
1966 Jan 01
Pagination:
155

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution Code:
A - Approved For Public Release
Distribution Statement: Public Release

RECORD

Collection: TRECMS
Identifying Numbers
Contract Number(s):
Nonr 233(76)
Project Number(s):
944-144
Subject Terms
Modernization Areas:
Fully Networked C3
Communities of Interest:
C4I
Descriptor(s):
military research, complex numbers, real numbers, theses, algebra, mathematics, coordinate systems, equations, numbers, united states, california, contracts, decomposition, eigenvectors, orthogonality, symmetry, united states government
Keyword(s):
DECOMPOSITION THEOREMS
Subject Categories:
Mathematical and Computer Sciences
Update Date:
2021 Jul 19