As a simple example, the matrix of a linear operator with respect to a basis is a rectangular array T that transforms under a change of basis matrix R = ( R i j ) by T ^ ^ = R − − 1 T R . For the individual matrix entries, this transformation law has the form T ^ ^ j ′ i ′ = ( R − − 1 ) i i ′ T j i R j ′ j so the tensor corresponding to the matrix of a linear operator has one covariant and one contravariant index: it is of type (1,1).