eigenvalue

Let $V$ be a vector space over $k$ and $T$ a linear operator on $V$. An eigenvalue for $T$ is an scalar $\lambda$ (that is, an element of $k$) such that $T(z)=\lambda z$ for some nonzero vector $z\in V$. Is that case, we also say that $z$ is an eigenvector of $T$.

This can also be expressed as follows: $\lambda$ is an eigenvalue for $T$ if the kernel of $A-\lambda I$ is non trivial.

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

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