NAME
    determinant - returns the scalar determinant of a square matrix

SYNOPSIS
      float determinant( float1x1 A );
      float determinant( float2x2 A );
      float determinant( float3x3 A );
      float determinant( float4x4 A );

PARAMETERS
    A       Square matrix of which to compute the determinant.

DESCRIPTION
    Returns the determinant of the square matrix *A*.

REFERENCE IMPLEMENTATION
    The various determinant functions can be implemented like this:

      float determinant(float1x1 A)
      {
        return A._m00;
      }
  
      float determinant(float2x2 A)
      {
        return A._m00*A._m11 - A._m01*A._m10;
      }
  
      float determinant(float3x3 A)
      {
        return dot(A._m00_m01_m02,
                   A._m11_m12_m10 * A._m22_m20_m21
                 - A._m12_m10_m11 * A._m21_m22_m20);
      }
  
      float determinant(float4x4 A) {
        return dot(float4(1,-1,1,-1) * A._m00_m01_m02_m03,
                     A._m11_m12_m13_m10*(  A._m22_m23_m20_m21*A._m33_m30_m31_m32
                                         - A._m23_m20_m21_m22*A._m32_m33_m30_m31)
                   + A._m12_m13_m10_m11*(  A._m23_m20_m21_m22*A._m31_m32_m33_m30
                                         - A._m21_m22_m23_m20*A._m33_m30_m31_m32)
                   + A._m13_m10_m11_m12*(  A._m21_m22_m23_m20*A._m32_m33_m30_m31
                                         - A._m22_m23_m20_m21*A._m31_m32_m33_m30));
      }

PROFILE SUPPORT
    determinant is supported in all profiles. However profiles such as fp20
    and the ps_2 manpage without native floating-point will have problems
    computing the larger determinants and may have ranges issues computing
    even small determinants.

SEE ALSO
    the mul manpage, the transpose manpage

