Question

If A=USV', then U orthogonally diagonalizes 
(a) AA'
(b) A'A
(c) A²
(d) (A')²​

Answer 1

Answer:

A is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix {\displaystyle P}P and a diagonal matrix {\displaystyle D}D such that {\displaystyle P^{-1}AP=D}{\displaystyle P^{-1}AP=D}, or equivalently {\displaystyle A=PDP^{-1}}{\displaystyle A=PDP^{-1}}. (Such {\displaystyle P}P, {\displaystyle D}D are not unique.) For a finite-dimensional vector space {\displaystyle V}V, a linear map {\displaystyle T:V\to V}{\displaystyle T:V\to V} is called diagonalizable