Difference between tuple and row matrix In Munkres Analysis on Manifolds the author uses the word ''tuple spaces'' to refer to a special sort of vector space. Further down on the same page (page 6) he discusses the linear isomorphism that maps a tuple to a row matrix. 
I am greatly confused by this as I do not understand the difference between a tuple and a row matrix and also I do not know what a tuple space is. I do know linear algebra and I do know the definition of a vector space. 
Please could someone help me understand this?

There is a formal difference between the tupel space 
$$
\mathbb R^n:=\mathbb R \times \dots \times \mathbb R
$$
and the space of row vectors $\mathbb R^{1,n}$, which is defined as the space 'numbers arranged in a row' (think arranged in a spreadsheet). In the book you linked, the difference is emphasized by using different kinds of brackets: $(x_1,\dots,x_n)$ in the former, $[x_1,\dots,x_n]$ in the latter case.
The spaces are defined differently first. Then one shows that they are isomorphic. This means in terms of linear algebra they are equivalent.
