What are Eigenvectors and Eigenvalues?

Eigenvalues are associated with eigenvectors in Linear algebra. Both terms are used in the analysis of linear transformations. Eigenvalues are the special set of scalar values that is associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed as characteristic roots. It is a non-zero vector that can be changed at most by its scalar factor after the application of linear transformations. And the corresponding factor which scales the eigenvectors is called an eigenvalue.