D.matrix {matrixcalc} | R Documentation |
Duplication matrix
Description
This function constructs the linear transformation D that maps vech(A) to vec(A) when A is a symmetric matrix
Usage
D.matrix(n)
Arguments
n |
a positive integer value for the order of the underlying matrix |
Details
Let be an
matrix with 1 in its
element
.
and zeroes elsewhere. These matrices are constructed by the function
T.matrices
. The formula for the
transpose of matrix is
where
is the column vector in the order
identity
matrix for column
. The function
u.vectors
generates these vectors.
Value
It returns an matrix.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Magnus, J. R. and H. Neudecker (1980). The elimination matrix, some lemmas and applications, SIAM Journal on Algebraic Discrete Methods, 1(4), December 1980, 422-449.
Magnus, J. R. and H. Neudecker (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, Second Edition, John Wiley.
See Also
Examples
D <- D.matrix( 3 )
A <- matrix( c( 1, 2, 3,
2, 3, 4,
3, 4, 5), nrow=3, byrow=TRUE )
vecA <- vec( A )
vechA<- vech( A )
y <- D %*% vechA
print( y )
print( vecA )