Geodesic
Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations
Filomat, Tome 34 (2020) no. 8, p. 2601

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Some necessary and sucient conditions for the existence of the -skew-Hermitian solution quaternion matrix equations the system of matrix equations with -skew-hermicity, A1X = C1; XB1 = C2; A2Y = C3; YB2 = C4; X = X; Y = Y; A3XA 3 + B3YB 3 = C5; are established in this paper by using rank equalities of the coecient matrices. The general solutions to the system and its special cases are provided when they are consistent. Within the framework of the theory of noncommutative row-column determinants, we also give determinantal representation formulas of finding their exact solutions that are analogs of Cramer’s rule. A numerical example is also given to demonstrate the main results.
DOI : 10.2298/FIL2008601R
Classification : 15A03, 15A09, 15B33, 15A24
Keywords: Sylvester-type matrix equation, quaternion matrix, Moore-Penrose inverse, noncommutative determinant, Cramer’s Rule 
Abdur Rehman; Ivan Kyrchei; Ilyas Ali; Muhammad Akram; Abdul Shakoor. Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations. Filomat, Tome 34 (2020) no. 8, p. 2601 . doi: 10.2298/FIL2008601R
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     author = {Abdur Rehman and Ivan Kyrchei and Ilyas Ali and Muhammad Akram and Abdul Shakoor},
     title = {Explicit formulas and determinantal representation for {\ensuremath{\eta}-skew-Hermitian} solution to a system of quaternion matrix equations},
     journal = {Filomat},
     pages = {2601 },
     year = {2020},
     volume = {34},
     number = {8},
     doi = {10.2298/FIL2008601R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2008601R/}
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