Let A be an n n matrix with singular value vector = (1,... , 1).

Let A be an n × n matrix with singular value vector σ = (σ1,... , σ1). Prove that
(a) ||σ||∞ = ||A||2;
(b) ||σ||2 = ||A||F, the Frobenius norm of Exercise 10.3.16.
Remark: ||σ||2 (also defines a useful matrix norm, known as the Ky Fan norm.