Monthly Archives: January 2013

Symmetric 0-1 Matrices with All Eigenvalues Positive, Part 2

A recent post and question on math.SE ask for an intuitive proof of the fact that the identity is the only symmetric 0-1 matrix with all eigenvalues positive.  As I mentioned in that recent post, Robert Israel’s argument is quite nice, but … Continue reading

Posted in linear algebra, matrices | 4 Comments

A Simple Proof that the Largest Eigenvalue of a Stochastic Matrix is 1

A stochastic matrix is a square matrix whose entries are non-negative and whose rows all sum to 1.  The transition matrix for a finite-state Markov chain is a stochastic matrix, and so they are essential for tackling problems that can … Continue reading

Posted in linear algebra, matrices, probability | 15 Comments