Question: Problem 1: Suppose . is a matrix norm on Mn, induced by a vector norm on Cn. Prove that for any invertible S E Mn

Problem 1: Suppose . is a matrix norm on Mn, induced by a vector norm on Cn. Prove that for any invertible S E Mn it holds that the matrix norm . s is induced by a vector norm on C. (Recall the definition of | . |s; for all A E Mn we define || Alls := IS-'ASII.)

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