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Exact and least-squares solutions of a generalized Sylvester-transpose matrix equation over generalized quaternions
Author(s)
Jaiprasert, Janthip
Date Issued
January 1, 2024
Type
Article
Abstract
We have considered a generalized Sylvester-transpose matrix equation AXB + CXTD = E, where A, B,C, D, and E are given rectangular matrices over a generalized quaternion skew-field, and X is an unknown matrix. We have applied certain vectorizations and real representations to transform the matrix equation into a matrix equation over the real numbers. Thus, we have investigated a solvability condition, general exact/least-squares solutions, minimal-norm solutions, and the exact/least-squares solution closest to a given matrix. The main equation included the equation AXB = E and the Sylvester-transpose equation. Our results also covered such matrix equations over the quaternions, and quaternionic linear systems.
Citation
Electronic Research Archive, 32(4), 2789-2804, 2024