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.

Tagged under: Mathematics,matrix,theory,linear,algebra,positive,definite,square,root,spectral,theorem,complex,real,diagonal

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