Let's say that I have this data matrix, which describe measurements of temperature over 10 different weather stations:
$$H = \begin{bmatrix} -5 & -5 & -6& -10& -20& -3& -20& -25& -30& 6\\ -4 & -6 & -6& -9& -10& -2& -15& -20& -25& 6\\ -3 & -3 & -6& -10& -11& 1& -10& -15& -22& 4\\ -4 & -3 & -4& -4& -12& 2& -5& -10& -20& 7\\ -3 & -4 & -2& -1& -10& 5& 0& -5& -18& 9\\ 1 & -1& 1& 4& -4& 6& 2& 1& -15& 10\\ 0 & 0& 0& 5& -4& 7& 5& 5& -14& 15\\ 2 & 1& 1& 6& -2& 5& 10& 7& -13& 20\\ 3 & 2& 2& 7& -1& 4& 15& 10& -12& 30\\ 5 & 1& 3& 8& 0& 3& 20& 15& -5& 31 \end{bmatrix}$$
Where each column is measurement each day and each row is the weather station.
CODE:
H = [
-5 -5 -6 -10 -20 -3 -20 -25 -30 6;
-4 -6 -6 -9 -10 -2 -15 -20 -25 6;
-3 -3 -6 -10 -11 1 -10 -15 -22 4;
-4 -3 -4 -4 -12 2 -5 -10 -20 7;
-3 -4 -2 -1 -10 5 0 -5 -18 9;
1 -1 1 4 -4 6 2 1 -15 10;
0 0 0 5 -4 7 5 5 -14 15;
2 1 1 6 -2 5 10 7 -13 20;
3 2 2 7 -1 4 15 10 -12 30;
5 1 3 8 0 3 20 15 -5 31]
[U, E, V] = svd(H)
But what would $U$, $E$ and $V$ mean? Well, I know that $E$ is just scalars. But I don't know what kind if scalars they are. Are they scalars of temperature? Scalars of vectors in some weird spaces?
Can some one explain what $U$, $E$ and $V$ mean in this case?
The singular value decomposition is relevant when you see your matrix as a linear operator. If you just have rows of data, it is hard to imagine that the singular value decomposition will tell you anything about your data.