scalar

A scalar is just a single ordinary number, like 3, -0.5, or 7. The name sounds fancy, but it earns the word 'scalar' from what it does: it scales things. Multiply a vector by the scalar 2 and the vector doubles in length; multiply by 0.5 and it shrinks to half; multiply by -1 and it flips to point the opposite way. So a scalar is the dial you turn to make a vector longer, shorter, or reversed, without changing the line it lies along.

The contrast with a vector is the whole point. A vector carries both a size and a direction (think of an arrow), while a scalar carries only a size (just a number on the number line). In this domain scalars are almost always plain real numbers, so for now you can read 'scalar' as 'a real number used to stretch or shrink vectors'. They are the coefficients in every linear combination and the entries inside every vector.

A tiny example: take the vector v = (3, 1). The scalar 2 gives 2*v = (6, 2) — same direction, twice as long. The scalar -1 gives -v = (-3, -1) — same length, opposite direction. And the scalar 0 collapses any vector to the zero vector (0, 0), the single point at the origin.