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Mathematics-Online course: Linear Algebra - Normal Forms - Eigenvalues and Eigenvectors

Eigenvalue and Eigenvector


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A scalar $ \lambda$ is called eigenvalue of square matrix $ A$ if

$\displaystyle A v = \lambda v,\quad v\ne 0\,.
$

The vectors $ v \neq 0$ with $ Av = \lambda v$ are called eigenvectors associated with eigenvalue $ \lambda$. The set of the zero vector and of all eigenvectors associated with a given eigenvalue forms a vector space called eigenspace $ V_\lambda$ of $ \lambda$.


(temporary unavailable)

The following examples illustrate the possible cases for real $ 2\times2$-matrices.


The following examples illustrate the possible cases for complex $ 2\times2$-matrices.


  automatically generated 4/21/2005