R: K Matrix

K.matrix {matrixcalc} | R Documentation

## K Matrix

### Description

This function returns a square matrix of order p = r * c that, for an r by c matrix A, transforms vec(A) to vec(A') where prime denotes transpose.

### Usage

    K.matrix(r, c = r)

### Arguments

`r` | a positive integer row dimension
`c` | a positive integer column dimension

### Details

The r \times c matrices {\bf{H}}{}_{i,j} constructed by the function `H.matrices` are combined using direct product to generate the commutation product with the formula {{\bf{K}}_{r,c}} = ∑\limits_{i = 1}^r {∑\limits_{j = 1}^c {≤ft( {{{\bf{H}}_{i,j}} \otimes {{{\bf{H'}}}_{i,j}}} \right)} }

### Value

An order ≤ft( {r\;c} \right) matrix.

### Note

If either argument is less than 2, then the function stops and displays an appropriate error mesage. If either argument is not an integer, then the function stops and displays an appropriate error mesage

### Author(s)

Frederick Novomestky fnovomes@poly.edu

### References

Magnus, J. R. and H. Neudecker (1979). The commutation matrix: some properties and applications, The Annals of Statistics, 7(2), 381-394.

Magnus, J. R. and H. Neudecker (1999) Matrix Differential Calculus with Applications in Statistics and Econometrics, Second Edition, John Wiley.

### See Also

`H.matrices`

### Examples

    K <- K.matrix( 3, 4 )
    A <- matrix( seq( 1, 12, 1 ), nrow=3, byrow=TRUE )
    vecA <- vec( A )
    vecAt <- vec( t( A ) )
    y <- K %*% vecA
    print( y )
    print( vecAt )

[Package matrixcalc version 1.0-3 Index]