Talk:Spectral radius

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1 Proofs
2 Mistake?
- 2.1 Planar graphs
- 2.2 Mistake

[edit] Proofs

Much of the content of this article should be moved to a proof page, as per Wikipedia:WikiProject Mathematics/Proofs. See Category:Article proofs for examples of how other articles have done this. linas 15:12, 4 December 2005 (UTC)

[edit] Mistake?

I believe there is a mistake in proving the upper bound for gelfand's theorem p(A)<¦A^k¦^{1/k}+e , but it is easily fixed since an upperbound exists from the first lemma.

What is the source for the proof of Gelfand's Fomula? Please cite! —Preceding unsigned comment added by 81.172.140.37 (talk) 09:23, 14 February 2008 (UTC)

[edit] Planar graphs

I don't think that the given definition of spectral radius of a graph has to be limited to PLANAR graph. Do you? --achab 06:37, 19 April 2007 (UTC)

[edit] Mistake

The follwing statement

Gelfand's formula leads directly to a bound on the spectral radius of a product of finitely many matrices, namely $\rho(A_1 A_2 \ldots A_n) \leq \rho(A_1) \rho(A_2)\ldots \rho(A_n).$

is definitely not valid. Gelfand's formula cannot imply the specified bound on the spectral radius of a product of matrices simply because such a bound is not valid.

Example.

Let

$A_1=\begin{bmatrix} 0 & 2\\ 1/2 & 0 \end{bmatrix},\qquad A_2=\begin{bmatrix} 0 & 1/2\\ 2 & 0 \end{bmatrix}.$