Matrix form etc. form the basis vectors Only is needed since others are expressed in terms of When size of vector is , j levels of basis vectors are needed There are basis vectors corresponding to detail coefficients and 1 basis vector corresponding to sum coefficient at level     Transformation matrix H has these basis vectors as columns Transformed vector for data (row) vector Each step can be defined as multiplication by a matrix Composition of these matrices gives the final transformation matrix H is orthonormal Hence, inverse operation is easy