The commands Matlab[chol](X) and Matlab[chol](X, 'output'='R') use MATLAB® to compute the Cholesky factorization, R, of a MapleMatrix or MatlabMatrix, where transpose(R)*(R) = X. If X is not positive definite, then an error is returned.

When you specify the optional parameter, $'\mathrm{output}'='\mathrm{RP}'$, two values are returned.  The second value, P, is zero if X is positive definite; otherwise, P is 1+dimension(R).  The first value, R, is the largest dimension matrix such that transpose(R)*(R) = XX, where XX is the upper left corner of X, of dimension P.

For further details on the chol command, see the MATLAB® documentation.

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

$a≔\mathrm{Matrix}\left(\left[\left[1\,0\right]\,\left[0\,3\right]\right]\right)$

$a≔\left[\begin{array}{cc}1& 0\\ 0& 3\end{array}\right]$

$\mathrm{Matlab}\left[\mathrm{chol}\right]\left(a\right)$

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

$b≔\left[\begin{array}{cccc}3& 1& 3& 5\\ 1& 6& 4& 2\\ 6& 7& 8& 1\\ 3& 3& 7& 3\end{array}\right]$

$r,p≔\mathrm{Matlab}\left[\mathrm{chol}\right]\left(b\,'\mathrm{output}'='\mathrm{RP}'\right)$