广义诱导范数
Generalized Induced Norms
摘要：
让||.||是复数域C上所有n阶矩阵的代数M_n上的范数。矩阵理论中一个有趣的问题是“是否有两个范数||.||_ 1和||.||_ 2在C^n上，使得||A|| =max{||Ax||二：||x||_1=1}。我们将调查这个问题及其各个方面，并将讨论在何种条件下，||.||_第1项=||.||_ 2.
英文摘要：
Let ||.|| be a norm on the algebra M_n 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 C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
