EigenVectors

If A is a nxn matrix, v a vector and c a scalar, and the following holds for some c and some v:

Av = cv

Then we say that v is an EigenVector of the matrix A, and its associated EigenValue is c.

Interesting properties of EigenVectors:

If A is symmetric, then all its Eigenvalues are real (as opposed to complex).

If all values of A are non-negative, then there exist n linearly independent eigenvectors for A such that they all have norm 1 and are mutually orthogonal.

(there are more, cannot remember off the top of my head)