MathDB
Miklos Schweitzer 1950_8

Source: first round of 1950

October 2, 2008
linear algebramatrixsearchlinear algebra unsolved

Problem Statement

Let A \equal{} (a_{ik}) be an n×n n\times n matrix with nonnegative elements such that \sum_{k \equal{} 1}^n a_{ik} \equal{} 1 for i \equal{} 1,...,n. Show that, for every eigenvalue λ \lambda of A A, either ∣λ∣<1 |\lambda| < 1 or there exists a positive integer k k such that \lambda^k \equal{} 1
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