Vector and vector half operators

The vec (vector) operator takes a \(d \times d\) matrix and stacks the columns into a single vector of length \(d^2\). The vech (vector half) operator takes a symmetric \(d \times d\) matrix and stacks the lower triangular half into a single vector of length \(d(d+1)/2\). The functions invvec and invvech are the inverses of vec and vech i.e. they form matrices from vectors.

Usage

vec(x, byrow=FALSE)
vech(x)
invvec(x, ncol, nrow, byrow=FALSE)
invvech(x)

Arguments

x

vector or matrix

ncol,nrow

number of columns and rows for inverse of vech

byrow

flag for stacking row-wise or column-wise. Default is FALSE.

References

Magnus, J.R. & Neudecker H.M. (2007) Matrix Differential Calculus with Applications in Statistics and Econometrics (3rd edition), Wiley & Sons. Chichester.

Examples

x <- matrix(1:9, nrow=3, ncol=3)
vec(x)
#> [1] 1 2 3 4 5 6 7 8 9
invvec(vec(x))
#>      [,1] [,2] [,3]
#> [1,]    1    4    7
#> [2,]    2    5    8
#> [3,]    3    6    9