h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Linear Algebra - A893900
Author: GTBacchus - SubEd, Guru, Procrastinator, Keeper, etc. - U166086

This is one of those entries that springs forth, fully-formed, from my head at 4 in the morning. I won't submit it to PR until I've had a good night's sleep, and somebody tells me that I should. My fondest hope for it is that someone who hasn't already studied the subject reads it and doesn't hate it. The question I'd most like to have answered is whether it's readable and understandable. My favourite colour is brown, and I'm a Capricorn.

Good night.

BTW, I realize it's long, and has a couple of equations. If you look at it, and don't read it through, feel free to post and tell me that. I'd like to know just how scary it is, honestly.

GTBacchus I've drunk far too much wine at the moment, so I really am not competent to judge this entry, but I do know how to spell 'gauge'. It's one of those peculiar words which is not spelt the way it should be. I hope to have a look at the rest of this entry when I'm a bit more sober.

Cheers, Gnomon!

Hi GTB

Well I haven't studied the subject, and if it's for people like me I do think it could be improved and made more understandable amd 'readable' (whatever that means). For one thing, I find the tone at times comes across as ever-so-slightly patronising, as though I am a lesser mortal who must be talked down to and handed this Very Important Message about linear algebra.

I think you could help to dispel that impression by bringing in the What's It All For? section much earlier.

It's also a bit weird to someone like me to be told that you are going to describe linearity in terms of a non-linear example - the fuel gauge, an example which is complicated by the fact that it is supposed in theory to be linear but of course doesn't always work that way. Why not just give a linear example - there are lots of familiar ones to choose from - how about an analogue clock, or a domestic thermometer, or a cooker control, or something?

The other slightly offputting thing is the references to what you learn on a course - but perhaps it is people embarking on such a course who are your target audience, in which case it presumably wouldn't be offputting at all.

So while I do appreciate the spontaneity of the outpouring in the small hours, it's probably worth going back to it in daylight and taking another look.

I don't think you need the salivate/cringe business at all. I am left wondering what it's trying to say. And please don't tell people to be thankful, ok? They don't need that!

Of course I realise that I might not be the sort of person you want to write for, in which case you can happily ignore me completely. I am not at all qualified to review this entry, and I am merely recording my personal first impressions. Possibly no help to you at all - sorry about that.

Bels

Bels, hi! Thanks for commenting.

You mentioned a thing or two about who my target audience might be. I have in the entry: "The purpose of the entry is really to let a student know what they might expect to learn in the class", mostly because I don't know whether anyone would be interested enough in Linear Algebra to want to know what it's about without also wanting to study it. Maybe I'm wrong about that. The challenge in this entry is to write something that a non-math-geek might actually sit through. Maybe it's a pointless exercise; I dunno.

I could move the purpose section closer to the top, sure.



"For one thing, I find the tone at times comes across as ever-so-slightly patronising"

I definitely don't want to come across that way. Can you tell me where it does that, specifically?

I just would have liked to have had some idea of what to expect from Linear Algebra before I took the class, so I was trying to write something like that. I imagine someone who likes maths, but isn't learning anything beyond Calculus might be curious as to what some of those advanced courses are about, anyway. Maybe that person is my main target audience - someone who is somewhat math inclined, but might or might not ever take Lin Alg.



"I don't think you need the salivate/cringe business at all. I am left wondering what it's trying to say. And please don't tell people to be thankful, ok? They don't need that!"

On that point, I agree. The conclusion is weak, and will be rewritten. That particular paragraph can certainly be consigned to oblivion without any regrets.



"It's also a bit weird to someone like me to be told that you are going to describe linearity in terms of a non-linear example - the fuel gauge"

Well, I don't think that linearity seems like much of a property, except in contrast to non-linearity. Try to define a straight line without mentioning a curve, y'know? (Euclid tried: "A straight line lies evenly with the points on itself" - the least lucid sentence he ever wrote.)

One person (off h2g2) read that, and told me they liked the example, so I'm going to wait until I've seen more feedback on it.

Actually, I can see how it could be reworded a bit... keeping the contrast, but starting with the linear case, and then bringing up the non-linear... I'll work on it.



"The other slightly offputting thing is the references to what you learn on a course - but perhaps it is people embarking on such a course who are your target audience, in which case it presumably wouldn't be offputting at all."

Well, the entry is basically about what one learns in a Linear Algebra class. Should I change the title to reflect that?



"I am not at all qualified to review this entry, and I am merely recording my personal first impressions."

That makes your impressions all the more valuable. Sure, I can talk with math people about whether this or that equation is accurate, but I really want to know how it reads to an English Lit major!




GTB
to make revisions

I've made some big edits, mostly in places where Bels suggested. I also rewrote the conclusion, but haven't given it a yet, because I can't bring myself to just call it 'Conclusion'.


GTB

I've read through the entry now. It is technically very well-written, but I'm not sure I like the approach - it tells me that lots of stuff exists without telling me what it is for or how it works. To me, reading this is like going to a restaurant, reading the menu and then going home!

I do actually know a bit about the subject - I studied it at University level 25 years ago. But I've forgotten a lot of it and never was really sure what an Eigenvalue was.

After that criticism, the following will seem fairly trivial:

We do not attempt --> It does not attempt
liter --> litre
centimeter --> centimetre

There is a footnote on the expression (3,7,8) which looks confusingly like power of 5. Perhaps you could put a few words of English at the end of this sentence to avoid having the footnote sign on the expression.

Thanks for the small edits, Gnomon; I've fixed those.

I know what you mean about the "menu". I don't know; I don't want to make the entry longer. I guess I could write entries about some of the topics, covering them in more detail. Then I'd probably have a Uni Project on my hands. Trouble is, there's only so much you can say without being able to draw pictures. I could tell you what eigenvalues are, algebraically, and show you how to calculate them and everything, but the only way it will begin to make sense intuitively, is if I can show you a picture or two. (Or maybe that's just true for me, and I'm a visual thinker. )


Which sub-topics do you think need their own entries? Matrix multiplication, I'm sure. Determinants. Eigenvalues. Linear Transformations? Solving systems with matrices? There are also topics that I haven't mentioned, like Linear Independence/Dependence. Hmm.

How many entries does it take to make a Uni Project? I've never done one.


GTB

I don't like the idea of University Projects myself, because the entries do not go through Peer Review. I find that the folks in Peer Review have a huge knowledge of diverse topics and can often spot errors in entries on really obscure subjects. I don't feel that you get that in Uni Projects, so I have never done one.

Do you think this entry is PR-worthy, then?

You could certainly put it into PR if you want, and get some feedback there.

Instead, you could apply to the admissions office for a uni project, and get help with writing entries on different topics, or do them all yourself of course. If there were a few of you working on the project you could each peer-review the others' entries, which might work better.

If you write them all yourself you could still ask people you know are savvy to comment, or even go hunting for commentators, as I have done in the past even for PR entries where I got little response (whose topics were far more recondite for this site than yours is).

Your other option for now would be to leave it here for longer and see if you get more feedback, or leave it here and send people to it.

Time for some shameless plugging then, it sounds like!

Fantastic! Some of the topics should definitely have more detail though - probably only practical to do this as seperate entries though. I'd like to see somethign about calculating inverses of matrices - I'm sure my (first year!) course covered this.

Since you mention eigenvalues, might it not be worthwhile including something about the associated eigenvectors as well? In which case, it may make sense to write the eigenvalue equation as AX=lambdaX, which can then be reduced to the form given.

I'm afraid I glazed over for quite a bit of it (long words ...the matrix bit puzzled me (mainly because I've never stumbled across them properly before) I wonder about putting the vector part first but only because I remember vector maths so comparing vectors to matrices would make more sense than explaining matrices and then comparing them to vectors(?)

I know what you mean about things being simpler graphically ( I popped into excel and drew the two unresolvable equations graphically, I'm so used to seeing linear equations expressed as y=mx+c I couldn't picture them) I think if you want to make it a bit more accessable you should mention what the curves look like from looking at the equations (m=slope (-ve down, +ve up), c=intercept (where the line crosses the vertical axis)...I've met people on scientific degree courses who didn't get taught this at school)

I think for each example you need an example equation from a RL situation, just talking about equations without example applications seems a bit pointless, especially when the techniques are used in practical subjects like engineering.

So far as graphics go you could always do the same as Rita did with her topographic entry and create a website containing the graphics and link to it...otherwise I can see this becoming longer and longer?

I dunno - just my initial thoughts...

But creating a web site with graphics and linking to it is not allowed for edited entries, is it? So if you intend to send this into Peer Review, it should stand on its own without diagrams.

A860429 does it and got edited with the links intact...don't know whether its a one off though? I don't remember anyone mentioning it in the PR thread but I suppose thats because it is a graphical subject...like this one ?

I recently Subbed A850691, and asked for some diagrams. The entry worked without them, but the descriptions are so much clearer with them.

I think the same should apply in this case.

Wow, Dr J, that's a subbing job! Makes my current batch seem like nothing by comparison.

I'm just writing an entry on Matrix Multiplication. I'll post a link as soon as I have it up. I think the only topics that will really require diagrams are Linear Transformations and Eigenvalues (with eigenvectors, and eigenspaces...)


GTB

Generally looks good, though I'm not the person to ask about first impressions not knowing whats going on. Some technical points:

> (Systems containing zero equations are not very interesting.)

Looks like you might be making more of a point than you are. Maybe add in 'Although' at the start of this sentence.

> Generally though, if you have three unknowns, you'll need three equations, and so on.

I'm never sure if 'generally' means 'in general, and in all cases' or 'usually'. Usually you do need 3, but
you might be unlucky and get linearly dependent ones. Not sure how to phrase this so its precise but not unweildy.

Book flipping example is good. Could maybe explain a little more what the flip is. It might not be obvious that youre supposed to do the same hand motion whatever orientation the book is in. Maybe talk about it rolling away from you, or spit roasting it with the skewer parallel to your chest.

> a square matrix has as many eigenvalues as it has rows (or columns).

unless they are repeated...

> When a matrix has complex eigenvalues, they occur in complex conjugate pairs,

I'm sure thats true if the matrix has real entries, but don't think its true if it has complex entries.