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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>. 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.
[[category:Linear algebra]]
[[Category:Linear algebra]]