Singular Value Decomposition (SVD) and Polar Form

Abstract

In this section we assume that we are dealing with a real Euclidean space E . Let f: E → E be any linear map. In general, it may not be possible to diagonalize a linear map f . However, note that f * ∘ f is self-adjoint, since $$ leftlangle (f* rc f)(u),v rightrangle = leftlangle f(u),f(v) rightrangle = leftlangle u,(f* rc f)(v) rightrangle . $$