Eigen values and Eigen vectors

In linear algebra the concept of Eigen values and Eigen Vectors relate to how we as mathematicians define a vector space. In this vector space, we define scalars which are just numbers and vectors which have an associated direction and magnitude. Often times we use matrices to represent how the space is set up. If the action of a matrix on a (nonzero) vector changes its magnitude but not its direction, then the vector is called an eigenvector of that matrix. A corresponding scalar is associated with this vector and is called the eigen value. This is a rather abstract concept but it helps us map and quantify a space with many dimensions. In simple 2-d we can say eigen values of 1 to each of two eigen vectors (1,0) and (0, 1). Computers use these to shift and map images as well as alter them with great precision.