Wielandt's Theorem

Let the n×n matrix A satisfy the conditions of the Perron-Frobenius theorem and the n×n matrix C=c_(ij) satisfy


for i,j=1, 2, ..., n. Then any eigenvalue lambda_0 of C satisfies the inequality |lambda_0|<=R with the equality sign holding only when there exists an n×n matrix D=delta_(ij) (where delta_(ij) is the Kronecker delta) and


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Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1121, 2000.

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Wielandt's Theorem

Cite this as:

Weisstein, Eric W. "Wielandt's Theorem." From MathWorld--A Wolfram Web Resource.

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