Abstract: A matrix pair $\left( X_{0},Y_{0}\right) $ is called a Hermitian nonnegative-definite solution to the matrix equation if $X_{0}$ and $Y_{0}$ are Hermitian nonnegative-definite and satisfy $AX_{0}A^{\ast }+BY_{0}B^{\ast }=C$. 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.
Keywords: Hermitian nonnegative-definite solution, matrix equation, generalized inverse, singular value decomposition.
Classification (MSC2000): 15A06; 19A09
Full text of the article: