fastmatrix (version 0.5-7721)

comm.info: 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)

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 condensed = FALSE.

m

positive integer, row dimension.

n

positive integer, column dimension.

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.

References

Magnus, J.R., Neudecker, H. (1979). The commutation matrix: some properties and applications. The Annals of Statistics 7, 381-394.

See Also

commutation, comm.prod

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