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

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.

Transcribed Image Text:

Let A = 22 -1 2