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Re: Linear Algebra with Interactive Examples

#3
Scytale wrote:
Wed May 23, 2018 10:53 am
Oh what an excellent resource! I detested linear algebra and have only recently come around to not thinking of it as a monster.

TBH, I probably didn't put as much effort into it as I should have. The idea of being able to say, "Why, yes, I do know how to specify and transform position, facing, and motion in n-dimensional space -- doesn't everyone?" is sort of appealing in a terribly geeky way. :D

But I'd been bitten hard by the programming bug at the time. I think that was when I was writing the first version of my fuzzy logic DBMS in System/370 Assembly language, and it sort of ate my life for a while to the detriment of a lot of other things.

And now I'm suffering for it, with the inability to write a working 3D rotation function. Woe! Do not do as I did! Learn your linear algebra!

:lol:
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Re: Linear Algebra with Interactive Examples

#5
Damocles wrote:
Wed May 23, 2018 11:24 pm
I always have little cheat sheet as reference for simple transformation matrices in 2D space, as a quick compact overview. 3D transformation matricies basically then just extend the same concept.

https://en.wikipedia.org/wiki/Transform ... matrix.svg
https://www.alanzucconi.com/2016/02/10/ ... on-matrix/
That is a really nice resource, Damocles! The cheat-sheet is particularly slick.
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Re: Linear Algebra with Interactive Examples

#6
For me, the costs of not paying enough attention to linear algebra came when I tried to learn certain numerical methods which... well, suffice it to say, 'projection operators' did my head in. I think this all stems from my thinking that matrix multiplication is much too awkward and has no business in the otherwise very regular world of analysis..

I recently picked up Kreyszig's 'intro to functional analysis' which geneneralizes concepts like this and sneakily puts them in a language more similar to what I like about analysis. Now I too can say damned sexy things like "Only solutions lying in the nullspace of this operator are admitted...", which, let's face it, is basically Shakespeare.

Speaking of which, any book by Kreyszig is an amazing resource for learning the elements spanning pretty much all of geometry and analysis. I wish we'd used them as assigned texts in university. It's put in a language understandable by anyone in a technical field and doesn't overload you with inscrutable set notation that everyone else seems to love overusing.
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Re: Linear Algebra with Interactive Examples

#8
Mate I could talk about this all day. The two I've read/am reading are:

Introduction to Functional Analysis with Applications - I can't speak to quality of sources like the link, I borrowed this copy from my library. Libraries are the best.

Differential geometry - I got this one from Amazon, these Dover books are pretty good. While I'm on the topic, I'd definitely also recommend Aris and, if you're up for a challenge, Flanders' Differential Forms . Oh man I'm getting carried away here

(I don't have any online PDF's :P )

I've also seen Kreyszig's Advanced Engineering Mathematics on various people's shelves and briefly looked through it; this seems to be a comprehensive survey of all maths (analysis and algebra) that an undergraduate degree is likely to cover.
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Re: Linear Algebra with Interactive Examples

#10
Damocles wrote:
Thu Jun 07, 2018 9:27 am
They have already invented vector and matrix calculations all the way back in 2000!
(At a time when they still used modems and ink feathers)

Ha. You young'uns today will never enjoy the pleasure of handing your deck of punched cards to an operator, waiting for your job to be run, and eventually receiving your output which consists of several lines of extremely helpful remarks such as:

IKJEFT01 Anomalous input. Probable user error, correct and resubmit.

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