Eigenvectors and Eigenvalues
Eigenvectors  are used for understanding linear transformations.  In data analysis, we usually calculate the eigenvectors for a correlation or covariance matrix.  Eigenvectors are the directions along which a particular linear transformation acts by flipping, compressing or stretching. Eigenvalue  can  be referred to as the strength of the transformation in the direction  of eigenvector or the factor by which the compression occurs.