Difference between revisions of "Eigenvalue"
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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]]. | ||
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Revision as of 21:22, June 8, 2008
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 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.