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.