How to calculate a.aT using GLM?

I’d like to calculate the 3x3 matrix, what I get by multiplying a 3 dimensional vector a by a transposed. So what I’m looking for is:

x               x^2, xy, xz
y  *  x y z  =  xy, y^2, yz
z               xz, yz, z^2

How would you do this using GLM?

My problem is that:

  1. It seems that it cannot transpose vectors
  2. It seems that it cannot multiply 3x1 to 1x3 matrices together.

I know I can just fill in the positions by hand, but isn’t there a better way for it?