Let be a matrix with positive coefficients so that for all , 2, ..., , then has a positive eigenvalue , and all its eigenvalues lie on the closed disk
See alsoClosed Disk, Ostrowski's Theorem
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ReferencesGradshteyn, 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|AlphaFrobenius Theorem
Cite this as:
Weisstein, Eric W. "Frobenius Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FrobeniusTheorem.html