Changes

</math>

</math>

where <math>I</math> is the [[identity matrix]]. Solutions where <math>\boldsymbol{x} = \boldsymbol{0}</math> are trivial (simple) and are ignored. Therefore non trivial solutions occur only if <math>A - \lambda I</math> is a [[singular matrix]]. A singular matrix does not have an inverse, so its [[determinant]] must be 0. Setting the determinant to 0 produces <math>|A - \lambda I| = 0</math>. Expanding this gives the [[characteristic polynomial]]. This is a polynomial in <math>\lambda</math> and equal in degree that of the matrix A (i.e. a 3x3 matrix produces a cubic (degree 3) characteristic polynomial). The solutions to this equation are the eigenvalues of <math>A</math>.

where <math>I</math> is the [[identity matrix]]. Solutions where <math>\boldsymbol{x} = \boldsymbol{0}</math> are trivial (simple) and are ignored. Therefore, non trivial solutions occur only if <math>A - \lambda I</math> is a [[singular matrix]]. A singular matrix does not have an inverse, so its [[determinant]] must be 0. Setting the determinant to 0 produces <math>|A - \lambda I| = 0</math>. Expanding this gives the [[characteristic polynomial]]. This is a polynomial in <math>\lambda</math> and equal in degree that of the matrix A (i.e. a 3x3 matrix produces a cubic (degree 3) characteristic polynomial). The solutions to this equation are the eigenvalues of <math>A</math>.

===Eigenvectors===

===Eigenvectors===

</math>

</math>

==See Also==

==See also==

* [[Linear algebra]]

* [[Linear algebra]]

* [[Quantum Mechanics]]

* [[Quantum Mechanics]]

[[Category:Linear Algebra]]

[[Category:Linear Algebra]]