8.9 Rank of matrix

The rank of \(\mathbf{A}\) is dimension of row space of \(\mathbf{A}\) (space spanned by rows of \(\mathbf{A}\)) which equals the dimension of the column space of \(\mathbf{A}\) (space spanned by columns of \(\mathbf{A}\)).

• The rank is the maximum number of linearly independent columns of a matrix.
• A matrix is full rank if the rank of the matrix is equal to the number of columns.