rank (linear algebra)

The rank of a matrix \[A\], denoted as \[\rank(A)\], is the dimension of the vector space spanned by its columns, which just so happens to correspond to the maximal number of linearly independent columns of \[A\]. This, in turn is identical to the dimension of the vector space spanned by its rows, i.e. \[\rank(A)=\rank(A^{T})\].