Why is the Jacobi matrix not a matrix?

In a variety reading manual, they write:

Let $ W subset mathbb {R} ^ n $ to be an open whole and $ F: W rightarrow mathbb {R} ^ m $ a $ C ^ k operate so that for each point $ p in M: = F ^ {-1} ($ 0 the derivative $ DF (p): mathbb {R} ^ n rightarrow mathbb {R} ^ m $ rang $ m $. then $ M $ is a $ C ^ k-variable with dimension $ d = n – m $.

Should not the derivative be a function of the type $ DF (p): mathbb {R} ^ n rightarrow mathbb {R} ^ {m times n} $ ?

The first time I saw this, I realized that it was an error in the manual, but it seems to appear several times afterwards. Am I wrong?