`symmetrizer`

Symmetrizer matrix

Description

This function returns the symmetrizer matrix of order \(n\) which transforms, for every \(n\times n\) matrix \(\mathbf{A}\) , vec \((\mathbf{A})\) into vec \(((\mathbf{A} + \mathbf{A}^T)/2)\) .

Usage

symmetrizer(n = 1, matrix = FALSE)

Arguments

Argument	Description
`n`	order of the symmetrizer matrix.
`matrix`	a logical indicating whether the symmetrizer matrix will be returned.

Details

This function is a wrapper function for the function symm.info . This function provides the information required to create the symmetrizer matrix. If option matrix = FALSE the symmetrizer matrix is stored in three vectors containing the coordinate list of indexes for rows, columns and the values.

Warning: matrix = TRUE is not recommended, unless the order n be small. This matrix can require a huge amount of storage.

Value

Returns an \(n^2\) by \(n^2\) matrix (if requested).

References

Abadir, K.M., Magnus, J.R. (2005). Matrix Algebra . Cambridge University Press.

Magnus, J.R., Neudecker, H. (2007). Matrix Differential Calculus with Applications in Statistics and Econometrics , 3rd Edition. Wiley, New York.

Examples

z <- symmetrizer(n = 100)
object.size(z) # 319 Kb of storage

N100 <- symmetrizer(n = 100, matrix = TRUE) # time: < 2 secs
object.size(N100) # 800 Mb of storage, do not request this matrix!

# a small example
N3 <- symmetrizer(n = 3, matrix = TRUE)
a <- matrix(rep(c(2,4,6), each = 3), ncol = 3)
a
b <- 0.5 * (a + t(a))
b
v <- N3 %*% vec(a)
all(vec(b) == as.vector(v)) # vectors are equal!

symmetrizer