det#

Purpose#

Returns the determinant of a square matrix.

Format#

d = det(x)#

Parameters:: x (NxN matrix or KxNxN array) – matrix or array used to find the determinant.
Returns:: d (scalar or 1-dimensional array) – the determinant(s) of x.

Examples#

x = { 3 2 1,
      0 1 -2,
      1 3 4 };

d = det(x);

format /rd 3,0;
print "The determinant of d =" d;

The code above, produces:

The determinant of d = 25

Remarks#

x may be any valid expression that returns a square matrix (number of rows equals number of columns) or a K-dimensional array where the last two dimensions are of equal size.

If x is a K-dimensional array, the result will be a 1-dimensional array containing the determinants of each 2-dimensional array described by the two trailing dimensions of x. For example, for a 10x4x4 array, the result will be a 1-dimensional array of 10 elements containing the determinants of each of the 10 4x4 arrays contained in x.

det() computes an LU decomposition.

detl() can be much faster in many applications.