Quasi-orthogonal subalgebras of matrix algebras
Hiromichi Ohno

TL;DR
This paper explores the existence and structure of quasi-orthogonal subalgebras within matrix algebras, demonstrating their abundance and spanning properties in specific prime power matrix spaces.
Contribution
It establishes the existence of a large family of quasi-orthogonal subalgebras in matrix algebras of prime power dimensions and shows they span the entire algebra.
Findings
Existence of p^{2kn}-1/p^{2k}-1 such subalgebras
Subalgebras are isomorphic to M_{p^{k}}
These subalgebras span M_{p^{kn}}
Abstract
We investigate pairwise quasi-orthogonal subalgebras in which are isomorphic to for , and a prime number with . We prove there exist such subalgebras and they span .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Matrix Theory and Algorithms
