Eigenvectors

If A is a nxn matrix, v a vector with at least one non-zero element and c a scalar (possibly zero), 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. Note that if v is an eigenvector, then any multiple of v is an eigenvector, too (except 0v).

Interesting properties of Eigen Vectors:

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

If A is symmetric, 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)