Polar decomposition

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In mathematics, the polar decomposition of a square real or complex matrix A {\displaystyle A} is a factorization of the form A = U P {\displaystyle A=UP} , where U {\displaystyle U} is a unitary matrix, and P {\displaystyle P} is a positive semi-definite Hermitian matrix ( U {\displaystyle U} is an orthogonal matrix, and P {\displaystyle P} is a positive semi-definite symmetric matrix in the real case), both square and of the same size. It was first introduced by French engineer Léon Autonne in 1902. If a real n × n {\displaystyle n\times n} matrix A {\displaystyle A} is interpreted as a linear transformation...

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