Difference between revisions of "Eigenspace"
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(disambiguation of kernel) |
(geometric multiplicity) |
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The '''eigenspace''' of a square [[matrix]] <math>A</math> is the vector space [[span]]ned by all [[eigenvector]]s of a particular [[eigenvalue]]. | The '''eigenspace''' of a square [[matrix]] <math>A</math> is the vector space [[span]]ned by all [[eigenvector]]s of a particular [[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>. | + | 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. |
[[category:Linear algebra]] | [[category:Linear algebra]] | ||
Revision as of 18:26, May 2, 2010
The eigenspace of a square matrix is the vector space spanned by all eigenvectors of a particular eigenvalue.
Stated another way, the kernel of the matrix is called the eigenspace associated with . The dimension of the eigenspace is the geometric multiplicity of the corresponding eigenvalue.
