Cool! Thanks for fixing it and for writing such a good article!

]]>Yep, thanks for catching that, Mihai!

]]>So, an matrix would indeed be an morphism from the object to itself, but it can’t be the identity morphism unless it satisfies the identity properties. That is, given any matrix we have , and given any matrix we have . As it turns out, this uniquely identifies the usual identity matrix, but I’ll leave you to verify that as an exercise!

]]>(Just starting here, sorry if the question seems naive.)

]]>I’m glad it’s helpful. Unfortunately, I don’t have a great answer for you.

I was never really an analyst, and over the last ten years I’ve forgotten what further result I even intended this post to support. If I could remember, it might help pin down my own references. I’d been thinking it would come up in the Radon-Nikodym theorem for signed measures, but I don’t seem to have used the fact that they form a Banach space there.

I think, in general, that I learned most of this from Rudin’s *Real and Complex Analysis*, but I can’t seem to find where he proves the Banach property. It’s possible that I just needed it to be a normed linear space, but saw that I could get Banach and went ahead to show that on my own; it’s kind of an exercise, really. If the Rudin reference helps, great, but past that I have no real idea what other citation to use.

For nearly 100 y from the advent of General Relativity (GR) in 19015, no book author could advance accurately GR with all mathematical details. This is the reason, a large number of anxious reader still don’t understand GR to the appreciating level. Most physicists are badly unskilled in mathematics. In order to hide their incompetency they become more and more wordy. While a single equation can be more weighty than a dozen page of wordy writing. ]]>