Generalized Induced Norms
Abstract
Let ||.|| be a norm on the algebra Mn of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||1 and ||.||2 on Cn such that ||A||=max||Ax||2: ||x||1=1 for all A in Mn. We will investigate this problem and its various aspects and will discuss under which conditions ||.||1=||.||2.
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