The general Hermitian nonnegative-definite solution to the matrix equation AXA∗ + BY B∗ = C

Xian, Zhang (2005) The general Hermitian nonnegative-definite solution to the matrix equation AXA∗ + BY B∗ = C. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 21 (1). pp. 33-42. ISSN 0866-0174

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Abstract

Consider the matrix equation AXA∗ + BY B∗ = C. A matrix pair (X0, Y0) is called a Hermitian nonnegative-definite solution to the matrix equation if X0 and Y0 are Hermitian nonnegative-definite and satisfy AX0A∗ + BY0B∗ = C. We give necessary and sufficient conditions for the existence of a Hermitian nonnegative-definite solution to the matrix equation, and further derive a representation of the general Hermitian nonnegative-definite solution to the equation when it has such solutions. An example shows these advantages of the proposed approach.

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