An Algorithmic Approach To Solving B = BCX + YAB Using Quotient Spaces
Alex Taylor
TL;DR
This paper introduces an algorithm based on quotient space formulation to solve the matrix equation B = BCX + YAB, providing conditions for its solvability within the context of the Frobenius rank inequality.
Contribution
It develops a novel algorithm utilizing quotient spaces to construct solutions for the matrix equation and establishes conditions for solvability.
Findings
Algorithm successfully constructs matrices X and Y when conditions are met.
Provides necessary and sufficient conditions for the solvability of the matrix equation.
Enhances understanding of the Frobenius rank inequality through quotient space analysis.
Abstract
One well-known necessary and sufficient condition for equality in the Frobenius rank inequality due to Tian and Styan is that the matrix equation B = BCX + YAB be solvable for X and Y. We develop an algorithm to construct the matrices X and Y using a quotient space formulation of the Frobenius rank inequality, and provide several necessary and sufficient conditions for solvability.
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Taxonomy
TopicsMatrix Theory and Algorithms · graph theory and CDMA systems · Advanced Optimization Algorithms Research