- #1

- 97

- 0

## Homework Statement

Let A be a real nxn matrix with non-negative elements satisfying [itex]\sum_{j=0}^n a_{ij}=1.[/itex] Determine the spectral radius of A.

## Homework Equations

Denote spectral radius [itex]\varsigma(A)=max(\lambda_{i})[/itex]

We know [itex]\varsigma(A) \leq ||A||[/itex] for any norm || ||

**3. Attempt at the solution**

Well, we know:

||A||

_{1}[itex]\leq[/itex]n

||A||

_{2}[itex]\leq[/itex][itex]\sqrt{n}[/itex]

||A||

_{inf}=1

So, can't all we say is that [itex]\varsigma(A) \leq 1[/itex] ? Or can we say more?