Commutation Matrix

Forms an mn x mn commutation matrix which transforms \(vec({\bf A})\) into \(vec({\bf A}^{'})\), where \({\bf A}\) is an m x n matrix

Usage

commutation(m, n)

Arguments

m

integer; number of rows of A

n

integer; number of columns of A

Value

Commutation Matrix

References

Magnus, J. R. & Neudecker, H. (1979) Annals of Statistics 7 (2) 381-394

Author

Jarrod Hadfield j.hadfield@ed.ac.uk

Examples

commutation(2,2)
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    0    0    0
#> [2,]    0    0    1    0
#> [3,]    0    1    0    0
#> [4,]    0    0    0    1