Every complex number z can be written in polar form z = r (cos + i sin)

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Every complex number z can be written in polar form z = r (cosφ + i sinφ) where r is a nonnegative number and cosφ + i sinφ is a complex number of modulus 1.
a. Prove that any n x n matrix A admits a polar decomposition of the form A = PQ, where P is an n x n positive semidefinite matrix with the same rank as A and where Q is an n x n orthogonal matrix.

b. Find a polar decomposition A = PQ.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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