Difference between revisions of "Eigenvectors and Eigenvalues"
Jump to navigation
Jump to search
m (New page: 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> where <math>\la...) |
m |
||
| Line 3: | Line 3: | ||
:<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math> | :<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math> | ||
| − | where <math>\lambda</math> is [[complex number]]. | + | 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. | ||
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 06:19, June 7, 2008
An Eigenvector of a square matrix is a vector such that,
where 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.