Difference between revisions of "Eigenspace"
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Stated another way, the [[Kernel (geometry)|kernel]] of the matrix <math>A-\lambda{I}</math> is called the eigenspace <math>E_\lambda</math> associated with <math>\lambda</math>. The dimension of the eigenspace is the ''geometric multiplicity'' of the corresponding eigenvalue. | Stated another way, the [[Kernel (geometry)|kernel]] of the matrix <math>A-\lambda{I}</math> is called the eigenspace <math>E_\lambda</math> associated with <math>\lambda</math>. The dimension of the eigenspace is the ''geometric multiplicity'' of the corresponding eigenvalue. | ||
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Latest revision as of 14:34, July 28, 2016
The eigenspace of a square matrix <math>A</math> is the vector space spanned by all eigenvectors of a particular eigenvalue.
Stated another way, the kernel of the matrix <math>A-\lambda{I}</math> is called the eigenspace <math>E_\lambda</math> associated with <math>\lambda</math>. The dimension of the eigenspace is the geometric multiplicity of the corresponding eigenvalue.