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| − | {{merge|eigenvector}}
| + | #REDIRECT[[Eigenvectors and Eigenvalues]] |
| − | An '''eigenvalue''' of a square [[matrix]] <math>A</math> is a [[real|real number]] or [[complex number]] <math>\lambda</math> such that
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| − | :<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>
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| − | for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a [[eigenvector]]. The eigenvalues are the zeroes of a matrix's [[characteristic polynomial]].
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| − | The product of all the eigenvalues of a matrix equals the value of the matrix's determinant. Since a matrix is invertible if and only if the determinant is non-zero, it is invertible if and only if zero is not an eigenvalue.
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| − | 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>.
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| − | [[category:Linear algebra]]
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