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Least squares X =± X η * solutions to split quaternion matrix equation A X A η * = B
Author(s) -
Liu Xin,
Zhang Yang
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6033
Subject(s) - mathematics , quaternion , matrix (chemical analysis) , transpose , operator (biology) , combinatorics , mathematical analysis , pure mathematics , mathematical physics , algebra over a field , eigenvalues and eigenvectors , geometry , physics , quantum mechanics , biochemistry , materials science , chemistry , repressor , transcription factor , composite material , gene
In the paper, the split quaternion matrix equation A X A η * = B is considered, where the operator A η * is the η ‐conjugate transpose of A , where η ∈{ i , j , k }. We propose some new real representations, which well exploited the special structures of the original matrices. By using this method, we obtain the necessary and sufficient conditions for A X A η * = B to have X =± X η * solutions and derive the general expressions of solutions when it is consistent. In addition, we also derive the general expressions of the least squares X =± X η * solutions to it in case that this matrix equation is not consistent.