Why do we use the word "scalar" and not "number" in Linear Algebra?

Question

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?

Answer 1

If we multiply a vector by a positive number, the magnitude (length) of the vector changes. For example, if v is a vector, then 2v is a vector in the same direction as v which is twice as long as v, and (1/3)v is 1/3 the length of v. So, the number (scalar) is a scaling factor.