In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the MINIMUM number of coordinates needed to specify any point within it.[1][2] Thus a line has a dimension of ONE because only one COORDINATE is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitudeand longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is THREE-dimensional because three coordinates are needed to locate a point within these spaces.
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of basis vectors, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set. In more general terms, a basis is a linearly independent spanning set.