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An '''Eigenvector''' of a square matrix <math>A</math> is a vector <math>\boldsymbol{x}\in\mathbb{R}</math> such that,

An '''eigenvector''' of a square [[matrix]] <math>A</math> is a vector <math>\boldsymbol{x}\in\mathbb{R}</math> such that,

:<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>

:<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>

where <math>\lambda</math> is [[complex number]], known as a '''eigenvalue''. The eigenvalue is the zero of a matrix's [[charateristic polynomial]].

where <math>\lambda</math> is [[complex number]], known as a [[eigenvalue]]. The eigenvalue is the zero of a matrix's [[charateristic polynomial]].

All the eigenvectors of a particular eigenvalue [[span]] a vector space called the eigenspace.

All the eigenvectors of a particular eigenvalue [[span]] a vector space called the [[eigenspace]].

[[category:mathematics]]

[[category:mathematics]]