Linear Algebra on odwiki

[TheDunadan]

Hi everyone,

for some time now I started scribbling down notes on what could be useful to know on the subject of linear algebra for houdini users. But I ran into the problem of 'how to present' it.

There are basically two possibilites:

A ) Just a listing with the common definitions of the most important operations etc. with possibly a few following examples. Basically this would be a 'what it is and what it does' clarification.

B ) Including some more fundamental principles and explaining how & why an operation works. This would include a bit more theory and require the reader to have read the above text as I'd move from the basics to increasingly more complex subjects.

Both versions have their advantages: Someone who just wants to check what the inner Eucledian product of two vectors is, might be happy to find that it can be used to calculate the length of a vector.

He'd never know though why this is called the inner Euclidian product and and how this relates to the Eucledian space and the Cartesian frame. There are quite a few cases where we can caluculate some inner product, but the geometric interpretation is a fairly different one or worse there is none.

Personally I favour something like Version B, but I can understand if people say that they want something more like A. Since I hopefully have understood the linear algebra part I won't read it, but hopefully some of you will and therefore please tell me, what you'd prefer.

Jens

[TheUsualAlex]

A while back I went to some math pages to look up some math terms, there exist vocabularies that I've never even heard... Scary how much I don't know...

[stevenong]

So I'm the only one who wants the gist of it so I could quickly apply the math & continue working?

I'm happy with whichever version you put up.

Thanks Jens!

Cheers!

steven

[sibarrick]

All sounds good to me. I'd quite like the gist and maybe some links to where to find out more if more depth is required.

[michael]

how & why is always a good thing to have...

[RickWork]

how & why is always a good thing to have...

14988[/snapback]

yep, that's always the hardest in figuring out. That's why I voted for option B.

Cheers,

Rick

[edward]

Wow, that's a pretty tall order there. I guess it really does depend on the audience. I can see different types of people gravitating towards one or the other.

It's probably too much work but I tend to think there's a way to do both together. You need to explain everything in option B anyhow. So go ahead and do it and then repeat definitions where appropriate into wiki words. Then hopefully one can have a glossary/index of terms by the time you're done.

The challenging thing is to make it so that it doesn't read like a text book.

[TheDunadan]

It's probably too much work but I tend to think there's a way to do both together. You need to explain everything in option B anyhow. So go ahead and do it and then repeat definitions where appropriate into wiki words. Then hopefully one can have a glossary/index of terms by the time you're done.

14996[/snapback]

Part of the reason I was asking is that version B takes more time, but I don't mind doing it, as long as there are a few willing to read it. Adding a list with all the definitions is the smallest part.

The challenging thing is to make it so that it doesn't read like a text book.

14996[/snapback]

We'll see This is really more difficult than I first expected: the advantage though, many concepts can be explained in a rather visual way with the help of Houdini Many text books are so hard to follow as everything is kept rather abstract and usually examples of the real world are missing. Frequently I notice that there are quite a few people who can solve most complex math equations and alike, but haven't got any clue on what they are actually doing. I'll be happy if everyone know what he'd have to do and why he does, even if he doesn't quite know how to do it actually manually.

So far it seems most people prefer version B, but I'm gonna wait just a bit longer.

Jens

[AdamJ]

great idea.. having examples of using this stuff in houdini would be very useful. A lot of times I'd read the book, get the theory and then sit and try to figure out how to exactly use the stuff in a practical manner..

[TheDunadan]

Possibly a question that is hard to answer, but what do you think is better:

Explaining something first on simple level / easy to understand level and than rephrase it in a more abstract and general way. Or the other way around ?!

Trouble is the following: I could first explain all the basics in 3d space and intuitively most of us will associate with a vector a direction in 3d space. However this is just the simplest interpretation of a vector; vectors can be pretty much anything: they could just as well be polynom or a function.

The bad thing about this (and likely the reason almost any text book starts with the abstract level first) is: all too easily we'll associate all these things too closely with 3d space and I know from myself it's very hard to later loosen these associations again to understand that these things are way more general and can be used for different things as well.

Having spent some of my sparetime with things such as wavelet-compression-algorithms, tracking, 3d reconstruction from 2d image sequences, ODE-Solver etc. I'd like to show how we can use Linear Algebra to solve these things. Here we'll often move away from 3d space to solve our problems: we do a linear transformation into a space that allows us to deal with the problem in a more effecient way and once we solved the problems there we'll move back into 2d/3d space or whereever we started. All those things closlely relate to computer graphics really.

Put into other words, we'd somewhat restrict ourself by thinking only of 3d space in cartisian frame and the mathematical beauty of linear algebra is that it's such a precise language to describe many different things, yet use similar concepts and methods.

Comments on this welcome

Jens

edit: This happens when you start loosing the focus. Given that 90% of the time if we're not doing any coding or alike we'll deal with 3d space, I suppose for sake of simplicity I'll start with 3d space. There are good text books on linear algebra and function analysis around.

[mark]

this would be very beneficial but as AdamJ said its not always easy to apply the theory to practice, examples would definitely be good. thanks

[RickWork]

I think you're on to something here and I think everyone can contribute and benefit from this. Houdini is great for flushing out mathematical ideas graphically. I think if you offer an explanation of say a vector and then either via jpeg or hip file offer a graphical reprensentation of a vector it would be helpful. Of course this is just a simple example. Perhaps a better example would be explaining a normal vector and then using the PointSOP to demonstrate how we use it and manipulate it?

I think alot of houdini's "black art" can be explained via a linear algebra lesson in layman's terms with a houdini tutorial or hip file demonstrating the concepts. I can see this tutorial getting a lot of hits by myself and many others. This would sure make VOPS more friendly.

Slightly OT..

Yesterday I was trying to explain to someone about base jumping and how we approx our calculation if we can do the jump or not. What did I do? Yep, I sparked up houdini, setup a simple particle sim, piped it out to a copySop and proved that we would crash and break our face at said height. LOL

Rick

[Mario Marengo]

Well Jens... it looks like you've got your work cut out for you

Here's my CAN$0.2:

You're going to be covering a *lot* of concepts here; and things that may be second nature to you, are pretty much guaranteed to be impenetrable to some... and surprisingly, the reverse can also be true sometimes: things that you think need to be explained in excruciating detail because you anticipate it will be hard to understand, turn out to be easy to grasp by most, and you end up over-explaining (all of which I'm guilty of in various sections of the pages on Spaces, for example).

What to do?!

I think this problem will *always* exist no matter whether you choose approach 'A' or 'B' (although given the results of this poll, you should obviously start with something closer to 'B'), and there's really only one way to resolve it, and that is with *feedback* -- that is to say: "constructive criticism".

A full overview of linear algebra is a huge undertaking by any standard. And even though Jens is willing to do all the principal work in this case, we (the community) *have* to get involved if we also want it to benefit us as much as I know we all want it to. How often do we get to influence what goes into a book??!? -- it's a damned rare opportunity and we should take advantage. We have this forum to do just that; but it has yet to be used in that way... and I'd like to encourage people to start doing so. To put it bluntly: speak up; let the author know what is or isn't (or is partially, or insufficiently) making sense to you. And do it publicly (in this forum) so that counter-arguments are also given a chance, and together form some kind of concensus. How often do we get to play "Editor", huh?

Some of this already goes on behind the curtains among the people who frequently contribute to the wiki, and it is very helpful, but the whole experience would be enriched tenfold if it opened up to include all the different levels of experience in the community.

I can't speak for anyone else, but I for one would welcome comments like, "This bit doesn't make sense to me", or "That part is *so* verbose I fell asleep half way through it", or "I *think* I get it but it would really hit home if I had a sample application, or maybe a graphic to go along with it" (in which case someone other than the author could volunteer to supply said graphic/sample), etc.

After that kind of feedback, it could very well end up being a weird, eclectic mixture of 'A' and 'B' -- a little bit of 'A' over here; a little 'B' over there -- but a mixture that works. After all; nobody wants "yet-another-textbook", right? We want a Houdini-centric viewpoint with real-world applications...

My point? It's pretty much impossible to predict what will work for such a specific target audience; esp. for such a large topic as this, so it needs everyone's input (ditto for Spaces, VexPointClouds, WhatIsAMatrix? or *anything* else in the wiki).

P.S: For anyone who read this far and is still awake... the above is a *shining* example of over-explaining a concept that is dead-simple to grasp!

Cheers!

[Marc]

I read it all and think its a great idea. BTW, there is also the talk page on the wiki, so people can put comments up there. Might be a little better because then you're commenting on that page only instead of spending a paragraph desciribing which section of the wiki you're referring to .

Ciao

M

[TheDunadan]

Thanks for all the feedback so far. And yep, I'll be most happy for feedback and corrections. If someone thinks the whole thing moves into the wrong direction, let me know about it. And to all those who know linear algebra anyhow, please correct me.. chances are good I'll do a booboo or two

One part I'm a bit worried is that I don't know all the proper english math terms and this makes the whole thing a bit tricky for me. Second problem, english itself... though I spent a year in the UK it's really a mix of colloquial english on the one hand side and english found in scientific papers (even in germany papers get usually written in english). Trouble is, if I stick to the typical 'scientific paper style' it's all very dry and likelyl be as difficult to read or worse than text books on this subject ... on the other hand side once I sent a rough sketch to poor Mario and my attempt in combining colloquial english with a more abstract subject wasn't much of a success I hope that this time I'll find a better mixture, but feel free to tell me if it's hard to understand.

And there is one last thing: naming conventions and symbols. Unfortunally there is no 'ISO' on this ... hopefully the one I'll use (and make an extra page for) will be easy to follow, if anyone knows of a good one however that most of you are used to, please tell me (I find the one on mathworld terrible, but if everyone else likes that one it would be fine with me).

I suppose I'll do the largest part somewhere around the christmas hollidays but if I find some spare time, I'll try to continously contribute to the VectorAlgebra Section on odwiki.

Jens

[edward]

That's an excellent point, Mario. I think the approach calls for TheDunadan to just spend the initial time putting in the notes that he has. That's a minimal amount of work and likely just as useful as any other approach.

[mark]

Herr Dunadan you shouldn't worry about the English skills. Either your English is excellent or babelfish has improved a lot since I last used it

[Jason]

I just wanted to say I'm really appreciating the new Wiki information, Jens - very nice to see indeed.

[lorduk]

Have you ever seen a houdini user that would say: "naah, I don't want know how this works!"

We do the things easy way: by knowing what we are using so detailed explenations are always useful (especially when they are well structured so you clud take what you need and come back when you have the time for readin up on something specific)

-Kaspar