vector function

Vector and vector half operators

The vec (vector) operator takes a $d x d$ matrix and stacks the columns into a single vector of length $d^2$. The vech (vector half) operator takes a symmetric $d x d$ 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.

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)
invvec(vec(x))