The triangulant
Tam\'as Bencze, P\'eter E. Frenkel
TL;DR
This paper introduces the triangulant of matrices, explores its relation to orthogonal eigenvectors, and applies it to characterize mutually unbiased bases, extending the concept to higher orders for invariant subspaces.
Contribution
It presents the novel concept of the triangulant, links it to eigenvector orthogonality and mutually unbiased bases, and generalizes it to higher orders for invariant subspace analysis.
Findings
Triangulant relates to orthogonal eigenvectors.
Provides a new characterization of mutually unbiased bases.
Generalizes to higher order triangulants for invariant subspaces.
Abstract
We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants of two matrices, and relate them to the existence of nontrivially intersecting invariant subspaces of complementary dimensions.
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Taxonomy
TopicsMatrix Theory and Algorithms · Algebraic structures and combinatorial models · Holomorphic and Operator Theory