What would it be to say that a linear map $T:\mathbb R^{m+n}\longrightarrow \mathbb R^n$ has maximal rank?
I'd like a precise definition of it, I skimmed several linear algebra books after the definition but I didn't find it.
If someone could recommend me a reference which defines it I would be glad=)
Thanks
The rank of a linear transformation $T$ is the dimension of the image of $T$, that is, the dimension of the set $$\{T(\alpha) \ | \ \alpha \ \text{is in the domain of $T$} )\}.$$ This set can be proved to be a subspace of the range of $T$. Now in your case, $T$ is mapped to $\Bbb R^n$. Note that if $A$ is a subspace of a vector space $V$, then $\dim A \le \dim V$. And also note that $\dim \Bbb R^n = n$. I think you can formulate for yourself what is meant by maximal dimension here. I don't think it's a standard term, though, to be found in books.