# 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