Sufficient Conditions for the Second Largest Characteristic Value of a Non-Negative Matrix (Numerical Solution of Partial Differential Equations and Related Topics)
Kazuo Kishimoto · Institutional Repositories DataBase (IRDB) · 2000
It is shown that if a matrix with real components maps any "mono- tone non-decreasing vector" to a "monotone increasing vector," the matrix has a "monotone increasing characteristic vector," and the modulus of corresponding characteristic value is the second largest among the moduli of characteristic values of the matrix.This propo- sition is proved as a corollary to more general propositions.Some other corollaries to these general propositions are also remarked.