Generate expansion matrix.
expan(d)Dimension of the expansion matrix. A positive integer.
The output is a matrix.
An expansion matrix that has dimension d ^ 2 by d * (d + 1) / 2.
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).
Henderson, H. V., and Searle, S. R. (1979). Vec and Vech operators for matrices, with some uses in Jacobians and multivariate statistics. Canadian J. Statist. 7, 65 - 81.