> An array of real numbers is not itself a vector. It is a representation of a vector in a particular basis. No, such an array can be either a vector or the re

> An array of real numbers is not itself a vector. It is a representation of a vector in a particular basis. No, such an array can be either a vector or the representation (which also has to be a vector) you mentioned. To make such things make sense, need a definition of a vector space. It can be tempting to omit that definition from an outline, but the definition is just crucial, e.g., when talking about subspaces, which is often crucial. E.g., for m x n matrix A and n x 1 'vector' x, the set of all x such that Ax = 0 is a subspace, but to know this need the definition of a vector space.