# 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?