On 2-dimensional invariant subspaces of matrices
Omar Al-Raisi, Mohammad Shahryari
TL;DR
This paper introduces a unified approach to analyze 2-dimensional invariant subspaces of matrices and explores their connection to super-eigenvalues, with applications to non-commutative algebra involving matrices over rings.
Contribution
It presents a novel method for studying 2D invariant subspaces and links eigenvalues of matrices over rings to these subspaces, advancing understanding in non-commutative algebra.
Findings
Unified method for 2D invariant subspaces
Connection between eigenvalues over rings and invariant subspaces
Application to non-commutative algebra
Abstract
We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of matrices with entries in the ring Mat_2(F) and 2-dimensional invariant subspaces of matrices with entries in the field F.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms