Suppose we have some vector space, say $V$; vectors $\bf v, u$ such that $\bf v,u$ are in $V$; and some scalars, call them $k,c$
So, if I understood this correctly, following operations
$$\tag 1 \mathbf{u} + \bf v$$
and
$$\tag2 k\bf u$$
do not necessarily mean usual addition or usual multiplication. In other words, when talking about vector space above, firstly we should define those two operations.
But what about these?
$$kc$$
$$k + c$$
Do these two operations mean usual scalar addition and usual scalar multiplication? Or should they be defined before considering vector space too?
Best Answer
The scalars come from a field. So there is already a notion of addition and multiplication.