I have a few doubts regarding vectors and linear algebra in general:
- What is the formal definition of a vector?
- When we say $\Bbb R^n$, do we mean the set of all column matrices with $n$ entries,or all row matrices with n entries, or all ordered $n$ tuples that is $(a_1,.....,a_n)$ ?
- If all members of a vector space are vectors, since $\Bbb R$ is a vector space, then it is implied that all real numbers are vectors. Is my understanding correct ?
- Geometrically, can we treat vectors as free or fixed? What is the correct convention?