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Positive Semi-Definite Matrix 1: Square Root

Matrix Theory: Let A be an nxn matrix with complex entries. Assume that A is (Hermitian) positive semi-definite. We show that A has a unique (Hermitian) positive definite square root; that is, a PSD matrix S such that S^2 = A. The key ingredient is the Spectral Theorem for C^n. Example in Part 2.
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