Description Usage Arguments Details Value References Examples
Generate expansion matrix.
1 | expan(d)
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d |
Dimension of the expansion matrix. A positive integer. |
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).
The output is a matrix.
expanMatrix |
An expansion matrix that has dimension d ^ 2 by d * (d + 1) / 2. |
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.
1 | expan(3)
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