| 释义 |
Perron-Frobenius theorem Perron-Frobenius theorem[pe′rōn frō′bā·nē·u̇s ‚thir·əm] (mathematics) If M is a matrix with positive entries, then its largest eigenvalue λ is positive and simple; moreover, there exist vectors v and w with positive components such that vM = λ v and Mw = λ w, if the inner product of v with w is 1, then the limit of λ -n times the i,j th entry of M n as n goes to infinity is the product of the i th component of w and the j th component of v. |