An eigenvalue is a coefficient of an eigenvector. By definition, an eigenvector is a non zero vector that only changes by a scalar factor when linear transformation is applied. In general, when linear transformation is applied to a vector, its span (the line passing through its origin) is shifted, but some special vectors are not affected by these linear transformations and remain on their own span. These are what we call eigenvectors. The linear transformation affects them only by stretching or squishing them as you are multiplying this vector with a scalar. The value of this scalar is called the eigenvalue. Let's say we have a matrix A, which will be used in linear transformation. We can represent the eigenvalue and eigenvector in a mathematical statements as follows:
Here, 
is the eigenvector and 
denotes the eigenvalue...
