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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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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