The contraction and expansion matrices are links between the "vec" operator and "vech"operator: for an d by d symmetric matrix A, vech(A) = contr(d) * vec(A), and vec(A) = expan(d) * vech(A). The "vec" operator stacks the matrix A into an d ^ 2 dimensional vector columnwise. The "vech" operator stacks the lower triangle or the upper triangle of a symmetric matrix into an d * (d + 1) / 2 vector. For more details of "vec", "vech", contraction and expansion matrix, refer to Henderson and Searle (1979).