Cross product of two vectors of unequal length

Question

I am trying to teach myself Bayesian statistics using the book Doing Bayesian Data Analysis by John Kruschke.

In the chapter on categorical variables in generalized linear models, the author explains that we get the interaction coefficient by multiplying the two coefficient vectors that pertain to predictor variables in the model.

He then proceeds to combine the vectors (-1,1) and (3,-2,-1) into a vector (-1,+2,-1, 1, -2, 1). I suppose this is a 'cross product' as opposed to a 'dot' product, but I really have no idea how it came to be. Could anybody explain to me on how such a combination happened?

If it helps, here is a link to the book.

If the link doesn't work, please see the following pictures:

So, in summary, I am interested in how was the cross product of the vectors $\beta_1$ and $\beta_2$ created.

Answer 1

The cross product would probably be notated $\vec \beta_1 \times \vec\beta_2$. This is instead $\vec \beta_{1 \times 2}$ and is referred to as "the interaction coefficients": it's not any kind of combination of the vectors $\vec\beta_1$ and $\vec\beta_2$, but rather its own separate vector giving the interaction effects between variables 1 and 2.