In linear algebra, things that are specified by a single number are scalars and things that are specified by a collection of multiple numbers are vectors (or higher-rank tensors).

This is wrong for at least two reasons. First, it blurs the distinction between a one-dimensional vector space over a field and field itself. Second, and perhaps more problematically, it gives the incorrect impression that (e.g.) if $\vec{V}(\vec{r}) = (V_x, V_y, V_z)$ is a vector field, then the individual component $V_x(\vec{r})$ is a scalar field and transforms accordingly under coordinate rotations.