EDB — 11N

Exercises

1. [11N]If $A\in {ℂ}^{m\times n}$ we can define the induced norms

   $$\begin{array}{}\text{(1)}& \Vert A{\Vert }_{p,q}\stackrel{.}{=}\underset{x\in {ℂ}^n,|x{|}_p\le 1}{max}|Ax{|}_q.\end{array}$$

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   Show that $\Vert A{\Vert }_{p,q}=\Vert \bar{A}{\Vert }_{p,q}$.