how to proof the sabinvariance theorem?
the sabinvariance theorem:
Let T be a non-negative irreducible matrix,s a positve number.and y>=.=0.a vector satisfying Ty<=sy.
Then (a) y>0;(b)s>=r,where r is the Perron-Frobenius eigenvalue of T.
Moreover,s=r if and only if Ty=sy.
- Planetary Bugs
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)
- Other useful stuff
new question: Prove a formula is part of the Gentzen System by LadyAnne
new question: A problem about Euler's totient function by mbhatia
new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia
new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz
new correction: Misspelled name by DavidSteinsaltz
new correction: underline-typo by Filipe
new correction: cocycle pro cocyle by pahio
new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier
new image: expected waiting time by robert_dodier
new image: plot W(t) = P(waiting time <= t) by robert_dodier