H.matrices {matrixcalc} | R Documentation |
List of H Matrices
Description
This function constructs and returns a list of lists. The component of each sublist is derived from column vectors in an order r and order c identity matrix.
Usage
H.matrices(r, c = r)
Arguments
r |
a positive integer value for an order r identity matrix |
c |
a positive integer value for an order c identify matrix |
Details
Let be the order
identity matrix
with corresponding unit vectors
with one in
its
th position and zeros elsewhere.
Let
be the order
identity matrix
with corresponding unit vectors
with one in
its
th position and zeros elsewhere.
The
matrix
is used in the computation of the commutation matrix.
Value
A list with components
1 |
A sublist of |
2 |
A sublist of |
...
r |
A sublist of c components |
Each component of sublist
is a matrix
Note
The argument n must be an integer value greater than or equal to two.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and applications, The Annals of Statistics, 7(2), 381-394.
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.
Examples
H.2.3 <- H.matrices( 2, 3 )
H.3 <- H.matrices( 3 )