Eigen Values and Vectors implications.

In linear algebra, an eigenvector or characteristic vector of a square matrix is a vector that points in a direction which is invariant under the associated linear transformation.

Eigen values are often introduced in the context of linear algebra or matrix theory. Historically, however, they arose in the study of quadratic forms and differential equations.

The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and arises in such common applications as stability analysis, the physics of rotating bodies, and small oscillations of vibrating systems.