DETERMINANT Function

Calculates the determinants for matrices stored as lists of lists of arrays.

Usage

d = DETERMINANT(m)

Input Parameters

m — A p-element list of p-element lists of n-dimensional arrays all of the same dimensions bi (i = 0, ..., n–1): (m(j))(k) is the jk component of a matrix function defined on n-space. Such matrix representations occur naturally as Jacobians of functions represented by arrays (see Jacobian).

Returned Value

d — An n-dimensional array of dimensions bi: d represents the determinant function of the matrix function represented by m.

Keywords

None.

Discussion

Determinants can be used to evaluate systems of linear equations. If one component of m is a constant then it can be given as a scalar instead of an array.

Example

r = INTERPOL([0,9], 100)               ; Polar coordinate radius
t = INTERPOL([-!Pi, !Pi], 200)         ; Polar coordinate angle
x = r#COS(t)                           ; Cartesian coordinate x
y = r#SIN(t)                           ; Cartesian coordinate y
j = JACOBIAN(LIST(x, y), x=LIST(r, t)) ; Jacobian of transformation
SHADE_SURF_IRR, DETERMINANT(j), x, y   ; Jacobian determinant == r