Applications of Eigen Values and Eigen Vectors.

Electrical Engineering: 

The application of eigenvalues and eigenvectors is useful for decoupling three-phase systems through symmetrical component transformation.

Eigenvalues and eigenvectors allow us to “reduce” a linear operation to separate, simpler, problems. For example, if a stress is applied to a “plastic” solid, the deformation can be dissected into “principal directions”- those directions in which the deformation is greatest. Vectors in the principle directions are the eigenvectors and the percentage deformation in each principle direction is the corresponding eigenvalue.

Communication Systems: 

Eigen values were used by Claude Shannon to determine the theoretical limit to how much information can be transmitted through a communication medium like your telephone line or through the air. This is done by calculating the eigenvectors and eigenvalues of the communication channel (expressed a matrix), and then water filling on the eigenvalues. The eigenvalues are then, in essence, the gains of the fundamental modes of the channel, which themselves are captured by the eigenvectors.


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