duplication {MVT} | R Documentation |
This function returns a duplication matrix of order n
which transforms,
for a symmetric matrix x
, vech(x)
into vec(x)
.
duplication(n = 1)
n |
order of the duplication matrix. |
Returns an n^2 by n(n + 1)/2 matrix.
Magnus, J.R., and Neudecker, H. (1980). The elimination matrix, some lemmas and applications. SIAM Journal on Algebraic Discrete Methods 1, 422-449.
Magnus, J.R., and Neudecker, H. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition. Wiley, New York.
dmat <- duplication(3) a <- matrix(c( 1, 2, 3, 2, 3, 4, 3, 4, 5), nrow = 3) vech <- a[upper.tri(a, diag = TRUE)] vec <- dmat %*% vech as.vector(vec)