TOPICS
Search

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

 |c_(ij)|<=a_(ij)

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

 C=(lambda_0)/RDAD^(-1).

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Wielandt's Theorem

Cite this as:

Weisstein, Eric W. "Wielandt's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WielandtsTheorem.html

Subject classifications