Question: The Polar Decomposition: Prove that every invertible matrix A has a polar decomposition, written A = QB, into the product of an orthogonal matrix Q

The Polar Decomposition: Prove that every invertible matrix A has a polar decomposition, written A = QB, into the product of an orthogonal matrix Q and a positive definite matrix B > 0. Show that if det A > 0, then Q is a proper orthogonal matrix.

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