Show that every square matrix A can be factored as A = RQ, where R is symmetric, positive semidefinite and Q is orthogonal.
Every complex number can be written in polar form as z = reiθ, where r = |z| is a nonnegative real number Thus, z has been decomposed into a stretching factor r and a rotation factor riθ. There is an analogous decomposition A = RQ for square matrices, called the polar decomposition.