Cramer’s rules for the system of quaternion matrix equations with η-Hermicity
Cramer’s rules for the system of quaternion matrix equations with η-Hermicity
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DOI：
10.1051/fopen/2019021
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发表时间：
2019
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影响因子：
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通讯作者：
Ivan Kyrchei
中科院分区：
文献类型：
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作者：
Ivan Kyrchei
本文考虑具有η-Hermity性质的双边四元数矩阵方程组，A1XA1η*=C1，A2XA2η*=C2。利用作者以前引入的非对易行列行列式，得到了系统通解的行列式表示(类似于Cramer法则)。作为特例，还讨论了当C_1=C_(η*1)和C_2=C_(η*2)时的η-Hermite解和当C_1=−C_η*1和C_2=−C_η*2时的−-斜厄米解的Cramer规则。
The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1, A2XA2η* = C2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η-Hermitian solution when C1 = Cη*1 and C2 = Cη*2 and for an η-skew-Hermitian solution when C1 = −Cη*1 and C2 = −Cη*2 are also explored.