You're right about that being wrong, and the author makes the same mistake consistently, but otherwise it looks correct. Some steps have details elided where it maybe should have been noted that things were being skipped, but with correct results. I think it's wonderfully written and a great exposition.
Thanks, that helps. When I notice errors in the stuff I already know about, it find it hard to trust the other information that’s new to me.
Re:What is the inverse of a vector?
by mferraro89 on Wednesday November 03, 2021 @12:40PM
(#29097048)
hey, if you have time to detail those mistakes I'd be happy to fix them in the text. Can you email me at [email protected]
He's not talking about the triplet or sextet, he means that a bivector has 5 degrees of freedom.
That isn't correct either though, the basis consists of three unit bivectors, so they have at most 3 degrees of freedom.
Re:What is the inverse of a vector?
by mferraro89 on Wednesday November 03, 2021 @12:39PM
(#29097033)
author here. I was mistaken about the 5 degrees of freedom bit. Bivectors have three. I'll fix the text tonight. I'm sorry you wasted ten minutes on my nonsense.
Hey, I thought it was wonderfully written. I'm definitely part of your target audience, as I fail to easily grok some algebraic concepts.
Thanks for taking the time to write it, and for making the notation easy to write and understand.
> It is important to remember that bivectors have a certain redundancy built into them in the sense that s a ⃗ ∧ b ⃗ = a ⃗ ∧ s b ⃗ s a ∧ b = a ∧s b . We can write them using 6 numbers or 3 numbers, but they actually convey 5 degrees of freedom.
Three (real) numbers have three degrees of freedom, by definition. (And nothing about complex numbers was mentioned.) Is this a parody I don’t get? I feel like I have wasted ten minutes on nonsense.