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In mathematical analysis, one of a set of discrete values of a parameter, *math.k*, in an equation of the form *math.L**x* = *math.k**x*. Such characteristic equations are particularly useful in solving differential equations, integral equations, and systems of equations. In the equation, *math.L* is a linear transformation such as a matrix or a differential operator, and *x* can be a vector or a function (called an eigenvector or eigenfunction). The totality of eigenvalues for a given characteristic equation is a set. In quantum mechanics, where *math.L* is an energy operator, the eigenvalues are energy values.

Learn more about eigenvalue with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Characteristic has several meanings:

- in mathematics
- characteristic function
- Euler characteristic
- characteristic (algebra)
- characteristic subgroup
- method of characteristics (partial differential equations)
- in physics and engineering
- any characteristic curve that shows the relationship between certain input- and output parameters, e.g.
- An I-V or current-voltage characteristic is the current in a circuit as a function of the applied voltage
- Receiver-Operator Characteristic
- Characteristic is the Greek word "χαρακτηριστικό" for a property|attribute (= trait) of an entity.

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Last updated on Monday September 08, 2008 at 16:51:53 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday September 08, 2008 at 16:51:53 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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