During a year and half of studying Linear Algebra in academy, I have never questioned why we use the word “scalar” and not “number”. When I started the course our professor said we would use “scalar” but he never said why.
So, why do we use the word “scalar” and not “number” in Linear Algebra?
So first of all, “integer” would not be adequate; vector spaces have fields of scalars and the integers are not a field. “Number” would be adequate in the common cases (where the field is R or C or some other subfield of C), but even in those cases, “scalar” is better for the following reason. We can identify c in the base field with the function ∗c:V→V,∗c(v)=cv. Especially when the field is R, you can see that geometrically, this function acts on the space by “scaling” a vector (stretching or contracting it and possibly reflecting it). Thus the role of the scalars is to scale the vectors, and the word “scalar” hints us toward this way of thinking about it.