comm.info {fastmatrix} | R Documentation |
Compact information to construct the commutation matrix
Description
This function provides the minimum information required to create the commutation matrix.
The commutation matrix is a square matrix of order mn
that, for an m\times n
matrix \bold{A}
, transform vec
(\bold{A}
) to vec
(\bold{A}^T)
.
Usage
comm.info(m = 1, n = m, condensed = TRUE)
Arguments
m |
a positive integer row dimension. |
n |
a positive integer column dimension. |
condensed |
logical. Information should be returned in compact form? |
Details
This function returns a list containing two vectors that represent an element of
the commutation matrix and is accesed by the indexes in vectors row
and col
.
This information is used by function comm.prod
to do some operations
involving the commutation matrix without forming it. This information also can be
obtained using function commutation
.
Value
A list containing the following elements:
row |
vector of indexes, each entry represents the row index of the commutation matrix. |
col |
vector of indexes, each entry represents the column index of the commutation
matrix. Only present if |
m |
positive integer, row dimension. |
n |
positive integer, column dimension. |
References
Magnus, J.R., Neudecker, H. (1979). The commutation matrix: some properties and applications. The Annals of Statistics 7, 381-394.
See Also
Examples
z <- comm.info(m = 3, n = 2, condensed = FALSE)
z # where are the ones in commutation matrix of order '3,2'?
K32 <- commutation(m = 3, n = 2, matrix = TRUE)
K32 # only recommended if m and n are very small