This picture illustrates the standard basis in R². The red and blue vectors are the elements of the basis; the green vector can be given with the basis vectors.

In linear algebra, a basis is a set of vectors in a given vector space with certain properties:

• One can get any vector in the vector space by multiplying each of the basis vectors by different numbers, and then adding them up.
• If any vector is removed from the basis, the property above is no longer satisfied.

The plural of basis is bases. For any vector space \displaystyle{ V }, any basis of \displaystyle{ V } will have the same number of vectors. This number is called the dimension of \displaystyle{ V }. view more...