Eigenvalue
Article
An eigenvalue is a scalar associated with a linear transformation or matrix. A nonzero vector is an eigenvector when the transformation changes only its magnitude or direction by multiplying it by that scalar.
Eigenvalues reveal characteristic modes of a mathematical or physical system. They can represent natural frequencies, growth rates, principal axes, energy levels, stability properties, or rates of decay.
For a square matrix, eigenvalues are found by solving the characteristic equation obtained from the determinant of the matrix minus a scalar multiple of the identity matrix. Repeated and complex eigenvalues can occur.
Eigenvalue methods are used in vibration analysis, quantum mechanics, differential equations, statistics, data reduction, fluid dynamics, control theory, networks, and numerical modelling.
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- Source / publisher: Wikipedia
- URL type: WWW
- Credits: Wikipedia
- URL: https://en.wikipedia.org/wiki/Eigenvalue