Hi Dan, thanks for taking the time to read this and leave your feedback. I'll try to address your remarks one-by-one. > I found the frequent self-quotes odd an

Hi Dan, thanks for taking the time to read this and leave your feedback. I'll try to address your remarks one-by-one. > I found the frequent self-quotes odd and the self-congratulatory introduction more odd. Thank you for the candid feedback! I have reflected a bit about this and where it comes from. It detracts from the main theme, which I regret, but also gives the reader context. Like many, I have flaws and ego is one of them. I try to be upfront about this, so the reader can bail early. > It starts with a paragraph which seems to be for someone who has never heard of graphs. This is a good point. I did not think very carefully about the audience. It is mostly, as you mention, a brain dump. At the same time, I am trying to explain some ideas which may be familiar to you, but others are encountering for the first time. I agree, this could be clearer what parts are for what audience. > this function must be linear and the numbers in a matrix are in some sense unimportant because they are relative to some basis Not attempting to be mathematically rigorous, but I think you raise an important point here, and I will try to clarify this point more carefully. Linearity can be a constraint in real vector spaces, but is less of a problem in Boolean algebra. The goal here is just to show how matrices can represent a function between vector spaces. > Then there’s a section about raising matrices to a power except when you look at it you realise it’s actually a product of different matrices. Not sure I follow, can you be more specific? I will try to clear this up. > The “matrix multiplications” in the section on data flow graphs don’t make sense to me, even with the random extra rules given above. Completely agree, this algorithm needs to be made more explicit, because it is a poorly written example. The full example can be found in Miller (1987). https://www.cs.cmu.edu/~glmiller/Publications/MRK86b.pdf https://www.cs.cmu.edu/~glmiller/Publications/MRK86b.pdf > I don’t want to be overly negative. Not at all! Again, thanks so much your comments. I would be happy to discuss them further here or by email.