A vector of dimension n is an ordered collection of an elements, which are called components.
Vector Spaces A vector space (over the real numbers) is a set V of
mathematical entities, called vectors, U, V, W, etc., in which an addition
operation “+” is defined and in which multiplication of vectors by
scalars i.e., real numbers.
We often represent a vector by some letter, just as we use a letter to denote a scalar (real number) in algebra.
A scalar is another name for "real number.".