Now look back at the second example program. We presented two versions of it. In the version in the left column, the matrix is of type MatrixXd which represents matrices of arbitrary size. The version in the right column is similar, except that the matrix is of type Matrix3d, which represents matrices of a fixed size (here 3-by-3). Because the type already encodes the size of the matrix, it is not necessary to specify the size in the constructor; compare MatrixXd m(3,3) with Matrix3d m. Similarly, we have VectorXd on the left (arbitrary size) versus Vector3d on the right (fixed size). Note that here the coefficients of vector v are directly set in the constructor, though the same syntax of the left example could be used too.