# detl¶

## Purpose¶

Returns the determinant of the last matrix that was passed to one of the intrinsic matrix decomposition routines.

## Format¶

y = detl()

## Examples¶

If both the inverse and the determinant of the matrix are needed, the following two commands will return both with the minimum amount of computation:

xi = inv(x);
xd = detl;


The function det(x)() returns the determinant of a matrix using the Crout decomposition. If you only want the determinant of a positive definite matrix, the following code will be the fastest for matrices larger than 10x10:

/*
** The 'call' keyword tells GAUSS to ignore the values
** returned from chol
*/
call chol(x);
xd = detl;


The Cholesky decomposition is computed and the result from that is discarded. The determinant saved during that instruction is retrieved using detl(). This can execute up to 2.5 times faster than det(x)() for large positive definite matrices.

## Remarks¶

Whenever one of the intrinsic matrix decomposition routines is executed, the determinant of the matrix is also computed and stored in a system variable. This function will return the value of that determinant and, because the value has been computed in a previous instruction, this will require no computation.

The following functions will set the system variable used by detl():

 chol(x) crout(x) croutp(x) det(x) inv(x) invpd(x) solpd(y, x) determinant of x