I’m not sure I should try writing this with a small television in my peripheral vision showing the first semi final match of this year’s US open… but I’ll try anyway. (That was yesterday.)
Let’s see. Last weekend I continued working on the next regression post. I got distracted from what I intended to write… and ended up describing the properties (computed by Mathematica®) of a regression. I had planned to introduce them piecemeal whenever I got around to discussing particular ones. Instead, I did what came naturally at the time… and begin a wholesale description.
I took it as a good omen later on in the week that someone asked on the Mathematica news group if it was a bug that “Response” held the given data y rather than the fitted values yhat. My discussion of all the properties might be useful.
I’ve been meaning to write about my “sense of wonder”, but there’s no hurry and I just haven’t done it. I’m still not going to talk about it today… except to say that the list of properties of a regression is an example of something that tickles my sense of wonder. Sometimes my fascination with mathematics boils down to, “What are they talking about?”
Of course, then I move on to, “Well, can I do that, too?”
There are still a couple of properties that I don’t understand. One of them, analysis of variance (ANOVA), is something I’ve played with a little bit over the years… but I can’t say I “get it”. The other property is called an eigenstructure table… and I don’t even know for sure what it is, nevermind what it’s good for. I’ll probably play with it a little bit today… to see if it is what I think it ought to be.
I was at the auto mechanic yesterday, and I brought along the latest aircraft control book (Yechout et al.). I was sorry to discover that, contrary to what I had thought, they do find it necessary to introduce the magic omega formula… “the following equation must be true”.
I’m just going to have to understand that equation!
I did start to describe that equation for this post… then I took a long break to watch the second mens’ semifinal match of the US Open.
And while I was taking that break, I decided that any discussion of the magic omega formula belongs in a technical post of its own. And I did get some ideas about how to investigate it. I might conceivably describe it in a technical post before I understand it, but I want to make at least some progress on it.
Since I am finishing up this post Sunday morning, I can say that my kid has been looking at matrix groups and at group theory in general.
Looking at material on matrix groups got me to thinking about a few of classifications:
- different forms of compactness
- different forms of submanifolds
- different matrix norms
- different matrix decompositions
I’d like to start working on describing and summarizing each of those.
Looking at group theory in general reminds me that it was my first love in pure mathematics… and I’d really like to get back to it.
Okay… time to get rolling today. I honestly haven’t decided if I’m going to do some mathematics first, or just dive into a blog post….