Let's imagine an arbitrary real n×n matrix, A. It is very possible that when we apply this matrix to some vector, they are scaled by a constant value. If this is the case, we say that the nonzero 
-dimensional vector is an eigenvector of A, and it corresponds to an eigenvalue λ. We write this as follows:
Note: The zero vector (0) cannot be an eigenvector of A, since A0 = 0 = λ0 for all λ.
Let's consider again a matrix A that has an eigenvector x and a corresponding eigenvalue λ. Then, the following rules will apply: ...
