Difference between revisions of "Eigenvectors and Eigenvalues"

Revision as of 20:02, June 8, 2008

An eigenvector of a square matrix $A$ is a vector ${\boldsymbol {x}}\in \mathbb {R}$ such that,

A{\boldsymbol {x}}=\lambda {\boldsymbol {x}}

where $\lambda$ 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.

@@ Line 1: / Line 1: @@
-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>
-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]]