Meaning A basis is a set of vectors that generates all elements of the vector space and the vectors in the set are linearly independent. More formally: Let V be a vector space over a fieldF. A subset M which generates the vector space V and which is a linearly independent subset is called a basis of vector space V. The subset M satisfies the linear independence property and the spanning property.
Examples Canonical basis {e1, e2, ... en} in F n
The figure shows the basis vectors i,j, k, and the vector a is a linear combination of them.
