by diagonalizing it.

Eigenvalues and eigenvectors give rise to many closely related mathematical concepts, and the prefix eigen- is applied liberally when naming them:
* The set of all eigenvectors of a linear transformation, each paired with its corresponding eigenvalue, is called the eigensystem of that transformation.
* The set of all eigenvectors of corresponding to the same eigenvalue, together with the zero vector, is called an eigenspace, or the characteristic