Matrices
Let Fm×n denote the set of matrices with entries in F. Then Fm×n is a vector space over F. Vector addition is just matrix addition and scalar multiplication is defined in the obvious way (by multiplying each entry by the same scalar). The zero vector is just the zero matrix. The dimension of Fm×n is mn. One possible choice of basis is the matrices with a single entry equal to 1 and all other entries 0.
Read more about this topic: Examples Of Vector Spaces