Abstract
The necessary and sufficient conditions for the existence and the explicit expression for the general solution are obtained for the quadratic matrix equation X*AX+B*X+D=0, where A∈Cn×n,B∈Cn×p and D∈Cp×p are given complex matrices with D*=D and A*=A, and (·)* denotes the conjugate transpose of a complex matrix. Furthermore, a type of inverse statistical problem which arises in satellite meteorology is discussed.
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