Let $\|\cdot\|$ denote any norm on $\mathbb{C}^{m}$ and also the induced matrix norm on $\mathbb{C}^{m \times m}$. Show that $\rho(A) \leq \|A\|$, where $\rho(A)$ is the spectral radius of $A$.

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Exercise 3.2

Let $∥⋅∥$ denote any norm on $ℂ^{m}$ and also the induced matrix norm on $ℂ^{m \times m}$ . Show that $ρ (A) \leq ∥ A ∥$ , where $ρ (A)$ is the spectral radius of $A$ .

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desh2608

2019-06-05 00:00

Exercise 3.2

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