| Line 1: |
Line 1: |
| − | {{merge|eigenvector}}
| + | #REDIRECT[[Eigenvectors and Eigenvalues]] |
| − | An '''eigenvalue''' of a square [[matrix]] <math>A</math> is a [[complex number]] <math>\lambda</math> such that
| |
| − | | |
| − | :<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>
| |
| − | | |
| − | 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 dimension of this space is called the '''geometric multiplicity''' of the eigenvalue.
| |
| − | | |
| − | [[category:Linear algebra]]
| |