Solution of linear matrix equations in a *-congruence class

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Roger A. Horn
Vladimir V. Sergeichuk
Naomi Shaked-Monderer


The possible *congruence classes of a square solution to the real or complex linear
matrix equation AX = B are determined. The solution is elementary and self contained, and includes
several known results as special cases, e.g., X is Hermitian or positive semidefinite, and X is real
with positive definite symmetric part.

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