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]].
  
[[category:mathematics]]
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[[category:Linear algebra]]

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.