Question: Prove that the spectral radius () is not a matrix norm on M n by giving examples of it failing to satisfy three of the

Prove that the spectral radius () is not a matrix norm on M_n by giving examples of it failing to satisfy three of the four properties required of a matrix norm (positivity, homogeneity, subadditivity, sub-multiplicativity), and prove that it satisfies one of these four

properties.

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