Eigenvalue

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An eigenvalue is a scalar associated with a linear transformation and a non-zero vector whose direction is unchanged by that transformation. The vector may be stretched, compressed, reversed, or left unchanged.

If a matrix A acts on a vector v so that Av = λv, then λ is an eigenvalue and v is a corresponding eigenvector. Eigenvalues are found by solving the characteristic equation det(A − λI) = 0.

A transformation can have several eigenvalues, repeated eigenvalues, complex eigenvalues, or no real eigenvalues. Their properties reveal important information about the transformation.

Eigenvalues are used in differential equations, stability analysis, vibration modes, quantum mechanics, statistics, graph theory, control systems, image processing, and many other areas.

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• Source / publisher: Wikipedia
• URL type: WWW
• Credits: Wikipedia
• URL: https://en.wikipedia.org/wiki/Eigenvalue