Scootertaj
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Homework Statement
Let A be a real nxn matrix with non-negative elements satisfying \sum_{j=0}^n a_{ij}=1. Determine the spectral radius of A.Homework Equations
Denote spectral radius \varsigma(A)=max(\lambda_{i})
We know \varsigma(A) \leq ||A|| for any norm || ||
3. Attempt at the solution
Well, we know:
||A||1\leqn
||A||2\leq\sqrt{n}
||A||inf=1
So, can't all we say is that \varsigma(A) \leq 1 ? Or can we say more?