Creating an equation library (Updated 03-FEB-2017)

[Han]

Looks like the SVD command uses EIGENVV to obtain the matrix V and to determine the diagonal matrix of eigenvalues. Letting M0 be the matrix I mentioned earlier, then EIGENVV(M0*trn(M0)) gives

Code:

M0:=[[3,4.5,4.5],[4.5,12.25,1.25],[4.5,1.25,12.25]];
EIGENVV(M0*trn(M0));

The result:

Code:

{
[
 [−0.426401432711,0.904534033733,4.07681407754ᴇ−17],
 [−0.639602149067,−0.301511344578,0.707106781187],
 [−0.639602149067,−0.301511344578,−0.707106781187]
],
[
 [272.25,0,0],
 [0,−7.5863407865ᴇ−32,0],
 [0,0,121]
]
}

So the middle eigenvalue for M0*trn(M0) is a negative value. Take the square root and you get the eigenvalue found from doing SVD(M0). Note that the real part was dropped (likely due to roundoff).

(−7.5863407865E−32)^.5 = 1.48466797577e−30+2.75433127755e−16*i

I wonder if within the SVD algorithm, forcing the diagonal matrix from the eigen-decomposition to have all positive entries (they necessarily have to be, since they are supposed to be squares), would provide a quick fix for this issue.

There is, of course, always the option of writing our own SVD...