<![CDATA[
#define M 3
#define N 3
int main() {
/* singular matrix rank(a) == 2 */
array double a[M][N] = {1, 2, 3,
4, 5, 6,
7, 8, 9};
int r = rank(a);
array double orth[M][r];
orthonormalbase(a, orth);
printf("rank(a) = %d\n", r);
printf("orth from orthonormalbase(a, orth) = \n%f\n", orth);
printf("transpose(orth)*orth = \n%f\n", transpose(orth)*orth);
}
]]>
<![CDATA[
rank(a) = 2
orth from orthonormalbase(a, orth) =
-0.214837 0.887231
-0.520587 0.249644
-0.826338 -0.387943
transpose(orth)*orth =
1.000000 -0.000000
-0.000000 1.000000
]]>