A vector is formally, an element of a vector space. A vector has two components: a direction (or vector) component and a scalar component. For example, gravity is vector: the direction of gravitational force on the earth is towards the center of the...

Abstract linear spaces are also called vector spaces, and they occur in a wide variety of mathematical settings. The most familiar examples are the finite dimensional Euclidean spaces. Let N be a positive integer. Then ℜN can be represented as the...

The primary example of a vector space is Rn, the set of ordered n-tuples of real numbers. If v = (v1,...,vn) w =(w1,..,wn) are elements of Rn then v + w is defined to be (v1 + w1,...,vn + wn). If r is a real number, then rv is defined to be (rv1,...

A linear space, also called a vector space, is a set with well-defined properties. First, a linear space must be defined over a field. This field is often the field of real numbers or the field of complex numbers, but may be other fields as well. The...

In mathematics, a collection of objects called vectors, together with a field of objects (&see; field theory), known as scalars, that satisfy certain properties. The properties that must be satisfied are: (1) the set of vectors is closed under vector...

In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. More formally, a vector space is a set on which two operations, called (vector) addition and (scalar)...