The eig command computes the eigenvalues of a matrix using MATLAB®.

If you specify the option 'eigenvectors'='true', then both the eigenvectors and the eigenvalues of the matrix are returned. The default is 'eigenvectors'='false'. In this form, the eigenvectors are the columns of the first matrix returned, and the eigenvalues are the entries along the diagonal of the second matrix returned.

If you specify the option 'balanced'='false', then a preliminary balancing step is not computed first. The balancing step  improves the conditioning of the matrix X. The default is 'balanced'='true'.

The call Matlab[eig](X, Y) solves the "generalized eigenvalue problem"; that is, it finds the roots of the polynomial $\det \left(\mathrm{lambda}Y-X\right)$.

By default a Vector of eigenvalues is returned. When you specify 'eigenvectors'='true', an additional Matrix of eigenvectors is also returned.

$\mathrm{with}\left(\mathrm{Matlab}\right)\:$

$\mathrm{maplematrix\_a}≔\mathrm{Matrix}\left(\left[\left[1\,2\,3\right]\,\left[3\,4\,5\right]\,\left[6\,7\,8\right]\right]\right)$

$\mathrm{maplematrix\_a}≔\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 6& 7& 8\end{array}\right]$

$\mathrm{Matlab}\left[\mathrm{eig}\right]\left(\mathrm{maplematrix\_a}\right)$

$\mathrm{vects},\mathrm{vals}≔\mathrm{Matlab}\left[\mathrm{eig}\right]\left(\mathrm{maplematrix\_a}\,'\mathrm{eigenvectors}'='\mathrm{true}'\right)\:$

$\mathrm{vects}$

$\mathrm{vals}$