FoReco (version 1.0.0)

commat: Commutation matrix

Description

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

Usage

commat(r, c)

Value

A sparse ($rc\times rc$) matrix, $\mathbf{P}$.

Arguments

r

Number of rows of $\mathbf{Y}$.

c

Number of columns of $\mathbf{Y}$.

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