Author Topic: itt we talk about MATRICES (and by 'we talk', I mean 'I talk to myself') (Read 1670 times)

recursivelyenumerable · « **on:** December 19, 2011, 01:48:50 AM »

I admit it, I kinda suck at linear algebra, or just basic matrix operations for that matter. I can never remember which is rows and which is columns and blah blah blah. So I'm going to abuse this message board to ramble to myself about matrices for a while.

OK. Go go go go go go go!

So an m X n matrix means m ROWS and n COLUMNS, right? And such a matrix represents a linear transformation between n-element vectors to m-element vectors, i.e. m X n matrix = n -> m transformation. So you need to mentally reverse the order of the indices ... which is confusing. But then if you put the n-element vector to the LEFT of the matrix and do matrix multiplication, thinking of it as a 1 X n matrix, the matrix does then act as an n -> m linear transformation ... but unfortunately, that goes against the usual convention where the operation goes to the left of the thing it's operating on (e.g. f(x), or even in normal algebraic notation for multiplication like 2x, the style kind of emphasizes the '2 ...' as an operation on x even though it could go either way).

Bebpo · « **Reply #1 on:** December 19, 2011, 01:50:09 AM »

I did some math in matrixes once a long long time ago. Was definitely fun in a puzzle solving playing with numbers way.

recursivelyenumerable · « **Reply #2 on:** December 19, 2011, 01:53:59 AM »

then, I guess the uhhhh monoid? (matrices, matrix multiplication) is uhhh homomorphic? to the monoid (linear transformations, composition). But again, what are the appropriate row/column orders and left/right ... nesses ... here?

recursivelyenumerable · « **Reply #3 on:** December 19, 2011, 02:00:28 AM »

So if we take an n -> m linear transformation, that corresponds to an n X m matrix put to the right of the vector it's transforming or an m X n matrix put to the left of the vector, we can compose it with an m -> uhhhh p-for-some-p transformation, to get an n -> p xformtion.

I guess

xAB : x in R^n, A is n X m, B is m X p, AB is n X p, xAB in R^p

or

BAx : x in R^n, A is m X n, B is p X m, BA is p X n, BAx again in R^p

ok, I think I get it. sort of. I'm sure this will last all of an hour or so and then I'll get confused again

recursivelyenumerable · « **Reply #4 on:** December 19, 2011, 02:01:34 AM »

now to try and understand conjugate gradient.

Pringo · « **Reply #5 on:** December 19, 2011, 02:19:07 AM »

To this day I think the spectral radius has the coolest name of any mathematical concept I've studied.

recursivelyenumerable · « **Reply #6 on:** December 19, 2011, 02:23:36 AM »

ooh, eigenvalues

recursivelyenumerable · « **Reply #7 on:** December 19, 2011, 02:31:30 AM »

So were you working with infinite-dimensional vector spaces, Pringo?

Pringo · « **Reply #8 on:** December 19, 2011, 02:37:20 AM »

Quote from: recursivelyenumerable on December 19, 2011, 02:31:30 AM

So were you working with infinite-dimensional vector spaces, Pringo?

iirc they were finite dimensional but it's been a while now so I can't say for sure.

recursivelyenumerable · « **Reply #9 on:** December 19, 2011, 02:39:55 AM »

you know, somehow eigenvalues make more sense to me when I think about them in terms of general abstract vector spaces than when I think of them in terms of general vectors in Euclidean space or something, guess I'm weird like that

Flannel Boy · « **Reply #10 on:** December 19, 2011, 03:14:33 AM »

Let off some steam, Bennett.

recursivelyenumerable · « **Reply #11 on:** December 19, 2011, 08:07:55 AM »

sleep is for the little people

T-Short · « **Reply #12 on:** December 19, 2011, 08:12:38 AM »

Don't remember much of matrix multiplications (Only that the transpose and determinant can only be defined for square matrices

). I remember loving linear algebra though, best part of the maths I took fo sho. recursive

Reb · « **Reply #13 on:** December 19, 2011, 08:20:13 AM »

Thought it said MAURICES.

recursivelyenumerable · « **Reply #14 on:** December 31, 2011, 06:25:59 PM »

just "lost it" AGAIN and trying to regain it by reading this thread. apparently I am just keeping my notes on evilbore from now on, hope demi maintains the archives & search feature well

Phoenix Dark · « **Reply #15 on:** December 31, 2011, 06:39:39 PM »

Quote from: Rebiak on December 19, 2011, 08:20:13 AM

Thought it said MAURICES.

each time I see this thread I think this :'(

Olivia Wilde Homo · « **Reply #16 on:** December 31, 2011, 06:45:42 PM »

I took Linear Algebra. Like Differential Equations, I got nearly a perfect score in the class because you have to realize that none of it makes any sense. The more you try to make sense of it, the more you get tangled up.

I still have no idea what eigenvalues and eigenvectors are.

recursivelyenumerable · « **Reply #17 on:** December 31, 2011, 06:49:41 PM »

the problem seems to be with my understanding of matlab syntax rather than my understanding of matrices themselves.

linear algebra and differential equations make NOTHING BUT sense. YOU don't make sense. unfortunately matlab doesn't make sense either

Pringo · « **Reply #18 on:** December 31, 2011, 06:52:47 PM »

Quote from: recursivelyenumerable on December 31, 2011, 06:49:41 PM

the problem seems to be with my understanding of matlab syntax rather than my understanding of matrices themselves.

linear algebra and differential equations make NOTHING BUT sense. YOU don't make sense. unfortunately matlab doesn't make sense either

I haven't worked in MATLAB in forever but isn't everything there defined to work with matrices and vectors by default? I remember the first time I used it it took me a while to realize how to use scalar values.

recursivelyenumerable · « **Reply #19 on:** December 31, 2011, 07:23:48 PM »

kinda, I think the problem really is that I just don't understand the scoping and precedence rules.

Van Cruncheon · « **Reply #20 on:** December 31, 2011, 08:16:50 PM »

yeah, of all math, linear algebra and diff calc have the most practical application and are the most sensible. on the other hand, laplacian transforms and e-fields

demi · « **Reply #21 on:** January 02, 2012, 10:13:05 AM »

Quote from: recursivelyenumerable on December 31, 2011, 06:25:59 PM

just "lost it" AGAIN and trying to regain it by reading this thread. apparently I am just keeping my notes on evilbore from now on, hope demi maintains the archives & search feature well

I am pretty confident that this is the only thread in the history of this message forum to have the word "Matrices"

MrAngryFace · « **Reply #22 on:** January 02, 2012, 10:27:55 AM »

It classes up the joint

tiesto · « **Reply #23 on:** January 02, 2012, 12:18:24 PM »

Never took Linear Algebra in school, so I was thrown in on the deep end when I had to convert a bunch of MATLAB routines to C++... but it wasn't too bad in the end. Just had to read some guides to do things.

Positive Touch · « **Reply #24 on:** January 02, 2012, 12:27:09 PM »

recursivelyenumerable · « **Reply #25 on:** January 08, 2012, 03:37:02 AM »

ok, it's an identity that (A' * B')' = B * A, right? I think? or something like that? and I understood WHY at one time, but now I will have to re-derive it AGAIN. but hey, the common trigonometric identities eventually sunk in for good after I re-explained them to myself for the 389th time, maybe these will too?

recursivelyenumerable · « **Reply #26 on:** January 08, 2012, 03:39:58 AM »

so A: Am -> An (YES I AM USING POSTFIX FOR FUNCTION APPLICATION)
B: Bm -> Bn

ugh not sure this will work though, I think "the transpose of a matrix" doesn't mean much to me other than a mechanical operation and that might be the real problem

recursivelyenumerable · « **Reply #27 on:** January 08, 2012, 03:42:24 AM »

maybe I should try thinking of 2x2 in geometric terms

like

x->x x->y
y->x y->y

x->x y->x
x->y y->y (transpose)

soooooooooooo transpose is about reversing the uhh "direction of contribution"?

recursivelyenumerable · « **Reply #28 on:** March 31, 2012, 10:40:06 PM »

still h8 matlab, but I have started resorting to using HUNGARIAN NOTATION to keep track of what is a column vector and what is a row vector, etc. Works surprisingly well in maintaining my sanity.

Madrun Badrun · « **Reply #29 on:** March 31, 2012, 11:09:23 PM »

wait you're having problems with matlab being column major?

recursivelyenumerable · « **Reply #30 on:** March 31, 2012, 11:17:30 PM »

I don't know what that means. Because Matlab is dynamically typed I tend to lose track of what orientation everything has, whether they're scalars or vectors or matrices, whether I need to transpose, etc.

Mandark · « **Reply #31 on:** April 01, 2012, 12:24:51 AM »

Quote from: recursivelyenumerable on March 31, 2012, 10:40:06 PM

Works surprisingly well in maintaining my sanity.

We'll be the judge of that, sir.

Van Cruncheon · « **Reply #32 on:** April 01, 2012, 07:38:20 PM »

i want to reply to this thread, but like so many computing related threads it makes me think of work and i go "ehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh"

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Author Topic: itt we talk about MATRICES (and by 'we talk', I mean 'I talk to myself') (Read 1670 times)