Suppose A C nn , show that there exist unitary matrix Q and semi positive definite Hermitian matrices H 1 and H 2 such that A H 1 Q QH 2 , where H 1 2 AA , H 2 A A This is known as the polar decomposition of matrix A and is often used in mechanics and materials science

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Question: Suppose A C nn , show that there exist unitary matrix Q and semi-positive definite Hermitian matrices H 1 and H 2 such that A

Suppose A Cⁿⁿ, show that there exist unitary matrix Q and semi-positive definite Hermitian matrices H₁ and H₂ such that A = H₁Q = QH₂, where H₁² = AA, H₂= AA. This is known as the polar decomposition of matrix A and is often used in mechanics and materials science.

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