Clojure Linear Algebra Refresher, Part 4: Linear Transformations

Post by joshstaiger » Mon, Jun 19, 2017, 4:47 PM UTC

btilly wrote: post #7

dragandj wrote: post #6

Earlier quoted context omitted.

I do not know whether you've read part 3 of this series. It explicitly treats matrix multiplication as function composition, and goes with this at length. As for the rest, you might be right or not; but I am not competent to reform world's math education. If you can write better linear algebra guides than the standard textbooks, I'm all for it. Please inform me if you do that, I'd love to read that. (BTW It's not sar…

I had not yet read it. Having just fixed it, it is missing the role of a basis. And without it, you'll have trouble figuring out coordinate systems, changing your basis, and so on. Which gives you no way to keep straight such confusing things as the fact that if your coordinate system rotates one way, your representation of things rotates the other. (Try it! Stand up, turn clockwise and see the world spin counter-clo…

I'm not sure if you'll see this 2 days later, but I've been trying to make heads or tails of your example and I think there’s a mistake in there somewhere.

Maybe I'm hopelessly lost, but, for one, the inverse of

    ( 1  1  1)
    ( 1  2  3)
    ( 1  2  4)

is not:

    ( 2 -1  0)
    (-3  2 -1)
    ( 1 -2  1)

On the off chance you see this, any pointers?

Post by btilly » Thu, Jun 22, 2017, 12:45 AM UTC

joshstaiger wrote: post #11

btilly wrote: post #7

Earlier quoted context omitted.

I had not yet read it. Having just fixed it, it is missing the role of a basis. And without it, you'll have trouble figuring out coordinate systems, changing your basis, and so on. Which gives you no way to keep straight such confusing things as the fact that if your coordinate system rotates one way, your representation of things rotates the other. (Try it! Stand up, turn clockwise and see the world spin counter-clo…

I'm not sure if you'll see this 2 days later, but I've been trying to make heads or tails of your example and I think there’s a mistake in there somewhere. Maybe I'm hopelessly lost, but, for one, the inverse of ( 1 1 1) ( 1 2 3) ( 1 2 4) is not: ( 2 -1 0) (-3 2 -1) ( 1 -2 1) On the off chance you see this, any pointers?

I did not see it.

As I commented in email, I did it by hand while very tired and made multiple mistakes.

Re: Clojure Linear Algebra Refresher, Part 4: Linear Transformations

Re: Clojure Linear Algebra Refresher, Part 4: Linear Transformations