Difference between revisions of "Eigenspace"
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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]]. | |
| − | + | 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]] |
Latest revision as of 14:34, July 28, 2016
The eigenspace of a square matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is the vector space spanned by all eigenvectors of a particular eigenvalue.
Stated another way, the kernel of the matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A-\lambda{I}} is called the eigenspace associated with . The dimension of the eigenspace is the geometric multiplicity of the corresponding eigenvalue.
