Difference between revisions of "Eigenvalue"
Jump to navigation
Jump to search
(n-dim space) |
(geometric multiplicity) |
||
| Line 6: | Line 6: | ||
for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}^n</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. | for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}^n</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>. | + | 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>. The dimension of this space is called the '''geometric multiplicity''' of the eigenvalue. |
[[category:Linear algebra]] | [[category:Linear algebra]] | ||
Revision as of 19:09, May 2, 2010
It has been suggested that this article or section be merged with [[::eigenvector|eigenvector]]. (Discuss)
An eigenvalue of a square matrix is a complex number such that
for some non-zero vector 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 is called the eigenspace of . The dimension of this space is called the geometric multiplicity of the eigenvalue.
