`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 \(\mathbf{A}\) , transform vec \((\mathbf{A}\) ) to vec \((\mathbf{A}^T)\) .

Usage

comm.info(m = 1, n = m, condensed = TRUE)

Arguments

Argument	Description
`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:

Value	Description
`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.

References

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

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

comm.info