I am confused by the singular value decomposition of a matrix. This may just be a misunderstanding of what singular value decomposition does so please be gentle with me. If I do a singular value decomposition on $X$ with $m$ rows and $n$ columns such that I get $X=U\Sigma V$. $V^*$ is supposed to be a nxn square matrix (see e.g. Wikipedia. However, for a matrix x e.g. size (40,100) I get in Julia (and also in R):
x = randn(40, 100) xsvd = svdfact(x) size(xsvd.Vt) (40,100)
I am expecting (100,100). However, for
x = randn(100, 40) xsvd = svdfact(x) size(xsvd.Vt) (40,40)
I get what I expect.
Can someone please explain to me what is going on here? And possibly point me to somewhere where I can read up on the fundamentals?