Spectral radius of a matrix

1. What is spectral radius of a matrix with example?
2. Is spectral radius a matrix norm?
3. Is spectral radius convex?

What is spectral radius of a matrix with example?

In mathematics, the spectral radius of a square matrix or a bounded linear operator is the largest absolute value of its eigenvalues (i.e. supremum among the absolute values of the elements in its spectrum). It is sometimes denoted by ρ(·).

Is spectral radius a matrix norm?

and by letting k tend to infinity we conclude that the joint spectral radius is well defined independently of the matrix norm used.

Is spectral radius convex?

Cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements.