# Matrices - How to compute reflectors

I was looking at this http://www.math.wsu.edu/faculty/watkins/pdfiles/francis.pdf

And it says that once you have the value of x you remove the zeroes and somehow create this

I have x and I can compute alpha, but I'm not sure how to generate this (3x3) reflector. I am trying to do this with code, so I'm ultimately looking for an algorithm/formula and not a "figure it out" type thing - the paper seems to suggest the existence of one with Theorem 1 but I can't figure out how to calculate the reflector.

• I'm trying to find the $\tilde Q_0$ you're talking about. I see a $Q_0$ in the slides, is that the same thing? Aug 26, 2016 at 21:57

Apparently, you mean equation (4) from the paper on page 393. You're supposed to build $\tilde Q_0$ directly using the fact that $\tilde Q_0 x = \alpha e_1$ and Theorem 1 on page 390.
• It's not that $Qx$ is equal to both, it's that you can choose a $Q$ for either one, and it doesn't matter which you choose. To find your $Q$, plug in your choice of $\|x\|e_1$ or $-\|x\|e_1$ to the formula. Aug 29, 2016 at 12:56