Difference between revisions of "Eigenvalue"
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(almost word for word the same as eigenvector) |
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:<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math> | :<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math> | ||
| − | for some vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a [[eigenvector]]. The eigenvalue is the zero of a matrix's [[charateristic polynomial]]. | + | for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a [[eigenvector]]. 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:Linear algebra]] | [[category:Linear algebra]] | ||
Revision as of 01:13, July 4, 2008
It has been suggested that this article or section be merged with [[::eigenvector|eigenvector]]. (Discuss)
An eigenvalue of a square matrix <math>A</math> is a complex number <math>\lambda</math> such that
- <math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>
for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a eigenvector. 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.