The vector pointing to x direction

i^ (i – hat)

The vector pointing to y direction

j^ (j – hat)

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.

Basis vectors

Set of *linearly independent* vectors that span the full space.

Basic of vector space

In linear algebra, the linear span (also called the linear hull or just span) of a set of vectors in a vector space is the intersection of all subspaces containing that set. The linear span of a set of vectors is therefore a vector space.

Span of vectors

In the theory of vector spaces, a set of vectors is said to be linearly dependent if one of the vectors in the set can be defined as a linear combination of the others;

Linearly independent vectors