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Let V be a finite-dimensional vector space over C and T in L(V) be an invertible...

Let V be a finite-dimensional vector space over C and T in L(V) be an invertible operator in V. Suppose also that T=SR is the polar decomposition of T where S is the correspondIng isometry and R=(T*T)^1/2 is the unique positive square root of T*T. Prove that R is an invertible operator that committees with T, that is TR-RT.

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