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
 |
Frobenius Theorem
See also
Closed Disk, Ostrowski's TheoremExplore 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
Frobenius TheoremCite this as:
Weisstein, Eric W. "Frobenius Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FrobeniusTheorem.html