Geodesic
The reducible solution to a system of matrix equations over the Hamilton quaternion algebra
Filomat, Tome 37 (2023) no. 9, p. 2731

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DOI

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology and others. In this paper, we investigate the reducible solution to a system of matrix equations over the Hamilton quaternion algebra. We establish the necessary and sufficient conditions for the system to have a reducible solution and derive a formula of the general reducible solution of the system when it is solvable. Finally, we present a numerical example to illustrate the main results of this paper.
DOI : 10.2298/FIL2309731L
Classification : 15A09, 15A24, 15B33, 15A03
Keywords: Matrix equation, Hamiltion quaternion, Reducible matrix, Moore-Penrose inverse, Rank 
Long-Sheng Liu; Qing-Wen Wang. The reducible solution to a system of matrix equations over the Hamilton quaternion algebra. Filomat, Tome 37 (2023) no. 9, p. 2731 . doi: 10.2298/FIL2309731L
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     title = {The reducible solution to a system of matrix equations over the {Hamilton} quaternion algebra},
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     year = {2023},
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     doi = {10.2298/FIL2309731L},
     language = {en},
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