I'm given the following description of the GCR algorithm:
I think I understand all the steps until: $$\beta = (v^i, r^{i -1})\\u^i:= u^{i-1} + \beta s^i$$
Question: What does $\beta s^i$ look like? Should I compute $\beta s^i = v^i s_1^i + r^{i-1}s_2^i$?
I'm confused as I don't really understand how you can define a vector by two row vectors; should it mean that $\beta$ is a matrix?
As pointed out correctly in the comments, $(v^i, r^{i-1})$ means $v^i\cdot r^{r-1}$. I checked the algorithm in python and using this interpretation everything works as expected.