Commutation matrix

This function returns the (\(r c \times r c\)) commutation matrix \(\mathbf{P}\) such that \(\mathbf{P} \mbox{vec}(\mathbf{Y}) = \mbox{vec}(\mathbf{Y}'),\) where \(\mathbf{Y}\) is a (\(r \times c\)) matrix (Magnus and Neudecker, 2019).

Usage

commat(r, c)

Arguments

r

Number of rows of \(\mathbf{Y}\).

c

Number of columns of \(\mathbf{Y}\).

Value

A sparse (\(r c \times r c\)) matrix, \(\mathbf{P}\).

References

Magnus, J.R. and Neudecker, H. (2019), Matrix Differential Calculus with Applications in Statistics and Econometrics, third edition, New York, Wiley, pp. 54-55.

See also

Utilities: FoReco2matrix(), aggts(), balance_hierarchy(), csprojmat(), cstools(), ctprojmat(), cttools(), df2aggmat(), lcmat(), recoinfo(), res2matrix(), shrink_estim(), teprojmat(), tetools(), unbalance_hierarchy()

Examples

Y <- matrix(rnorm(30), 5, 6)
P <- commat(5, 6)
P %*% as.vector(Y) == as.vector(t(Y)) # check
#> 30 x 1 Matrix of class "lgeMatrix"
#>       [,1]
#>  [1,] TRUE
#>  [2,] TRUE
#>  [3,] TRUE
#>  [4,] TRUE
#>  [5,] TRUE
#>  [6,] TRUE
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