Let V be a vector spaceMathworldPlanetmath over k and T a linear operatorMathworldPlanetmath on V. An eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath for T is an scalar λ (that is, an element of k) such that T(z)=λz for some nonzero vector zV. Is that case, we also say that z is an eigenvectorMathworldPlanetmathPlanetmathPlanetmath of T.

This can also be expressed as follows: λ is an eigenvalue for T if the kernel of A-λI is non trivial.

A linear operator can have several eigenvalues (but no more than the dimensionPlanetmathPlanetmath of the space). Eigenvectors corresponding to different eigenvalues are linearly independentMathworldPlanetmath.

Title eigenvalue
Canonical name Eigenvalue1
Date of creation 2013-03-22 14:01:53
Last modified on 2013-03-22 14:01:53
Owner drini (3)
Last modified by drini (3)
Numerical id 8
Author drini (3)
Entry type Definition
Classification msc 15A18
Related topic LinearTransformation
Related topic Scalar
Related topic Vector
Related topic Kernel
Related topic Dimension2
Defines eigenvector