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My book writes: A vector in $F^n$ may be regarded as a matrix $M_{n\times 1}(F)$. (true / false)

What is $F$ or $F^n$, and how does the notation $M_{m\times n}(F)$ work? The books also likes to use $M_n(\mathbb{R})$. That is referring to the same basic thing?

Thank you :)

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You have a vector space over a field, usually the field is denoted $F$ (F for Field of course).

$F^{n}$ is the Cartesian product $F\times...\times F$ ($n$ times), for example: the elements of $F^{2}=F\times F$ are all the pairs $(a,b)$ where $a,b\in F$ .

$M_{m\times n}(F)$ denotes all the $m\times n$ matrices with all entries in $F$.

Note that, for example, the elements of $M_{2\times1}(F)$ are of the form $\begin{pmatrix}a\\ b \end{pmatrix}$ where $a,b\in F$ so we can regard this like vectors in $F^{2}$ and vice versa

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    the point is, i don't have my book yet. just copies from the pages with the homework so far. my university is on a different continent than my highschool, and so the profs use things without mentioning them, that i never heard of before (different highschool education). So - yea. as soon as i got the books (wed), i'll go through the first pages for sure :P by the way, our books are: Friedberg, Insel and Spence, Linear algebra, 4th edition && R.A.Adams: Calculus, a Complete Course, 7th ed. @AndreaOrta2012-09-16