Talk:Matrix multiplication

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Contents 1 Dot products of vectors 2 Picture 3 HTML representation 4 Error in Kronecker Product Section 5 partitioned matrices 6 Notation 7 howto's belong in wikibooks 8 The coefficients-vectors method 9 proportions matrix?

[edit] Dot products of vectors

A good way to envisage matrix mult is to split the first into rows, the 2nd into columns, and vector dot-produc them. --anon

Matrix multiplication can also be envisages a dot products of vectors. The above example becomes::

The above is for the article, but trying to get the numbers right makes my brain ache. I'm leaving it here in case I've got them wrong. -- Tarquin 17:30 Jan 15, 2003 (UTC)

Perhaps it is good to work with column vectors; then the a's on the left must get a T for transposed. - Patrick 17:39 Jan 15, 2003 (UTC)

yup, that's the right way to do it.

I like that way a lot better than the other way, and I think the above general formula should be on the page. How I usually envision it is I write a horizontal line, then a verticle line, representing a lines of vectors. Its simpler to me to write a matrix of dotted vectors, rather than handle every element of the matrix separately. Fresheneesz 08:35, 21 March 2006 (UTC)

After reading over the "proportions-vectors method" I don't have any idea what it means by proportions.. Perhaps that should be explained better? Fresheneesz 08:37, 21 March 2006 (UTC)

"we take once the first vector and twice the third vector, while ignoring the second vector"

I'm pretty sure we're not gonna "ignore" anything, you multiplied the second vector by 0. I'm going to change that so it doesn't sound as .. vapid.. (no offense). Unless anyone argues. Fresheneesz 08:39, 21 March 2006 (UTC)

[edit] Picture

Okay, here's something that is probably one of these things that only makes sense to me.

When this picture was posted, it looked different. Find the original here.

it basically shows that the entries of the product matrix are filled in according to which row and column are multiplied. If anyone else gets it & thinks it useful for the article , please add it -- Tarquin 23:46 Jan 21, 2003 (UTC)

(except I've just realised the result matrix in the pic has the wrong number of rows .... hmmmmm. if there's a call for it I'll remake it)

Surely it makes sense to me also! This diagram uses unequal m and p, which is better (more general). I would use the diagram and add a third column for B in the example. - Patrick 01:14 Jan 22, 2003 (UTC)

Ah, that's good to know! There are many concepts in maths that I envisage pictorially in some way... and then I find that nobody else does... very disconcerting! Well, if one more person gets it, we'll put it in the article :-) -- Tarquin 23:03 Mar 14, 2003 (UTC)

This is the best illustration of matrix multiplication I've ever seen. In fact, I think it's one of the best math illustrations on Wikipedia. The second I saw it, I 'got' matrix multiplication for the first time. Beautiful work. Fredrik | talk 23:24, 10 Mar 2005 (UTC)

I fixed the picture, making it have correct number of rows. I also added yellow highlight around the elements that are being used, cause before it could have looked like only two elements were going into the new cell (the cells from which the arrow starts). Thats how I saw the picture so it confused me. I think the outline helps clarify that confusion. Fresheneesz 09:47, 21 March 2006 (UTC)

[edit] HTML representation

While I love HTML, the statement:

(the HTML entity ⊗ (⊗) represents the direct product, but is not supported on older browsers)

seems out of place. This article is about matrix multiplication, not HTML. Thoughts?

I've seen another article which had a simliar comment, and the consensus was to leave it because "people deserve to know how to write it" or something. I think its small, and should be at the end, but be there none the less. Fresheneesz 08:35, 21 March 2006 (UTC)

Thank you! I cannot imagine things pictorally well, and I always forget the algorithm for Matrix Multiplication. This picture is a lifesaver! wiki@matthewwilkes.name

[edit] Error in Kronecker Product Section

In the Kronecker product section, I believe there is an error.

Should be:

Right??

Yup. There should be an m. Fixed it. -- Tarquin 18:14, 22 Jun 2005 (UTC)

[edit] partitioned matrices

There needs to be some explanation of Partitioned matrix algrbra especially with respect to multiplication. I don' the math software so I hereby throw the ball to someone else. MPS 14:53, 20 Jun 2005 (UTC)

[edit] Notation

It is quite unusual to write AxB for the matrix product. AB or if necessary A.B is commonly used. Also, for multiplying numbers one uses 3x4 and not 3.4. The dot is used for the product of variables: a.b if just writing ab would lead to confusion.Nijdam 23:14, 28 February 2006 (UTC)

I agree that A × B for the matrix product is very uncommon, and I edited the article accordingly. However, I've encountered the notation 2 · 3 for the product of the numbers 2 and 3 quite often, so I left that one in. -- Jitse Niesen (talk) 11:20, 2 March 2006 (UTC)

[edit] howto's belong in wikibooks

wikipedia should just say what matrix multiplication is

[edit] The coefficients-vectors method

In the example, it jumps from [3 1]+[0 0]+[2 0] to [5 1] without any explanation. I've had every edit I've made to a math page reverted, so I will suggest here that an extra step be added to point out how you get from the first step to the next. It is [(3+0+2) (1+0+0)]. Without that, it is not obvious what is going on unless you already know matrix multiplication - and if you did, you wouldn't be reading this article. --Kainaw ^(talk) 14:57, 2 September 2006 (UTC)

[edit] proportions matrix?

In "properties, what the proportions matrix means?

The article either needs to explain or avoid this usage. The "proportions" matrix is the left-hand matrix and the "vector" matrix is the right-hand matrix. Paul D. Anderson 23:13, 6 October 2006 (UTC)