Difference between revisions of "Eigenvalue"

Latest revision as of 21:11, June 26, 2010

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-{{merge|eigenvector}}
+#REDIRECT[[Eigenvectors and Eigenvalues]]
-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]], the degree of the corresponding root is called the '''algebraic multiplicity''' of the eigenvalue.
-The [[span]] of all the eigenvectors corresponding to a fixed eigenvalue <math>\lambda</math> is called the [[eigenspace]] <math>E_\lambda</math> of <math>A</math>.
-[[category:Linear algebra]]