It depends on the ring of the matrix. For example, it works for matrices over `CDF`

:

```
sage: M = matrix(CDF, [[1,2,3],[1,4,6]])
sage: M.SVD()
(
[-0.455252372951 -0.890362441325]
[-0.890362441325 0.455252372951],
[ 8.17345734477 0.0 0.0]
[ 0.0 0.441129270439 0.0],
[ -0.164632267291 -0.986355015482 -2.81388521797e-16]
[ -0.547131320636 0.0913215509714 -0.832050294338]
[ -0.820696980953 0.136982326457 0.554700196225]
)
```

but not for matrices over `QQ`

:

```
sage: M = matrix(QQ, [[1,2,3],[1,4,6]])
sage: M.SVD()
AttributeError: 'sage.matrix.matrix_rational_dense.Matrix_rational_dense' object has no attribute 'SVD'
```

So, the method `.SVD()`

is not implemented for every kind of matrices.

Can you explain what you mean by use SVD directly? The commands you mentioned is the way to use SVD. Is there any other way you wish to do it?