MathDB

Problem 2

Part of 2011 SEEMOUS

Problems(1)

a_(ij)*a_(ji)≤0, eigenvalues of A=(a_(ij))

Source: SEEMOUS 2011 P2

6/18/2021
Let A=(aij)A=(a_{ij}) be a real n×nn\times n matrix such that An≠0A^n\ne0 and aijaji≤0a_{ij}a_{ji}\le0 for all i,ji,j. Prove that there exist two nonreal numbers among eigenvalues of AA.
matrixeigenvalueslinear algebra