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Ostrowski's Theorem

Let A=a_(ij) be a matrix with positive coefficients and lambda_0 be the positive eigenvalue in the Frobenius theorem, then the n-1 eigenvalues lambda_j!=lambda_0 satisfy the inequality

|lambda_j|<=lambda_0(M^2-m^2)/(M^2+m^2),
(1)

where

M=max_(i,j)a_(ij)
(2)
m=min_(i,j)a_(ij)
(3)

and i,j=1, 2, ..., n.

See also

Frobenius Theorem

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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

Ostrowski's Theorem

Cite this as:

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

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