Determinantal Representations of General and (Skew-)Hermitian Solutions to the Generalized Sylvester-Type Quaternion Matrix Equation
نویسندگان
چکیده
منابع مشابه
Ela Extreme Ranks of (skew-)hermitian Solutions to a Quaternion Matrix Equation∗
The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical matrix equation AXA +BY B = C over the quaternion algebra. Also given in this paper are the formulas of extreme ranks of real matrices Xi, Yi, i = 1, · · · , 4, in a pair (skew-)Hermitian solution X = X1 + X2i + X3j + X4k, Y =...
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The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical matrix equation AXA +BY B = C over the quaternion algebra. Also given in this paper are the formulas of extreme ranks of real matrices Xi, Yi, i = 1, · · · , 4, in a pair (skew-)Hermitian solution X = X1 + X2i + X3j + X4k, Y =...
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Expressions, as well as necessary and sufficient conditions are given for the existence of the real and pure imaginary solutions to the consistent quaternion matrix equation AXB+CY D = E. Formulas are established for the extreme ranks of real matrices Xi, Yi, i = 1, · · · , 4, in a solution pair X = X1 +X2i+X3j+X4k and Y = Y1+Y2i+Y3j+Y4k to this equation. Moreover, necessary and sufficient cond...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2019
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2019/5926832