Stacking vectors and matrices

Stacks either a lower triangle matrix or a matrix.

Usage

vec(x)
vech(x)

Arguments

x

a numeric matrix.

Details

The function vec implements the operator that stacks a matrix as a column vector, to be more precise in a matrix with one column. \(vec(X) = (X_{11}, X_{21}, ..., X_{N1}, X_{12}, X_{22}, ..., X_{NN})\).

The function vech implements the operator that stacks the lower triangle of a NxN matrix as an N(N+1)/2x1 vector: \(vech(X) =(X_{11}, X_{21}, X_{22}, X_{31}, ..., X_{NN})\), to be more precise in a matrix with one row.

Examples

## Create Pascal Matrix:
   P = pascal(3)
   
## Stack a matrix
   vec(P) 
#>       [,1]
#>  [1,]    1
#>  [2,]    1
#>  [3,]    1
#>  [4,]    1
#>  [5,]    2
#>  [6,]    3
#>  [7,]    1
#>  [8,]    3
#>  [9,]    6
   
## Stack the lower triangle
   vech(P)                                        
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    1    1    2    3    6