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The Perron-Frobenius theorem says that the largest eigenvalue of a positive real matrix (all entries positive) is real. Moreover, that eigenvalue has a positive eigenvector, and it is the only ...

This question is about the positive definiteness of a (non-random) matrix that is defined using random variables as follows: We fix the vector $v=(1,1)$ (yet, it seems the final result does not ...

My collaborators and I are studying certain rigidity properties of hyperbolic toral automorphisms. These are given by integral matrices A with determinant 1 and without eigenvalues on the unit circle....

Suppose I'm trying to estimate the spectral radius of a square $n \times n$ matrix $A$, and let $N$ be a distribution over Gaussian i.i.d. vectors of length $n$. Is the following lemma true: If the ...