There doesn’t seem to be any area for mathematics so for now I will put everything in one thread. Yesterday I was thinking about generalizing matrix multiplication to higher dimensions. I know this has already been done before (A.K.A.) tensors but I don’t know anything about tensors. Anyway I realized that there are three common types of multiplication that can be done on matrices. They are element wise multiplication, the inner product and the outer product. Many types of matrix multiplications can be expressed as a combination of these. For instance standard 2D matrix multiplication is a combination of the inner and outer product. The rows of matrix one and the columns of matrix two are used in the outer product while the columns of matrix one and the rows of matrix two are used in the inner product.

o_o;.. s243a, can you give us people who are only taking Geometry a little bit of information on this? I'm sure I could help, if only I knew what you meant exactly.. I mean, I can grasp it, but then it floats away.

There's no place like home.. there's no place like home..

Hey Birthday boy,
Forget geometry today and enjoy your day

Okay, well lets start with the basics. The inner product also known of as the dot product is the sum of element wise multiplication. For instance if you have two vectors [a b] and [c d] then the inner product is ac+bd and is denoted:



The operation is done by first doing element wise multiplication which I will denote as .* for example:


And then by taking the sum of the resulting vector.


The inner product is a measure of how close two vectors are, some applications include geometry and signal processing.

Matrix multiplication can be thought of as row by column multiplication. For instance.
Let:

and

If C is the Matrix product of A and B then:


Notice that an inner product of the rows of A are formed with the columns of B.
The outer product is the opposite of the inner product in the since that the size of the resulting matrix increases instead of decreases. For instance the outer product of the vector [a b] with [c d] is


Note that ac denotes a*c
Now lets distinguish between a row and a column vector. A row vector will be a horizontal vecor
For instance [a b]
And a column vector will be a verticale vector:

We will use a semi column to denote a new row so [c; d] will also be considered a column vector and [ac ad; bc bd] will be considered a 2 by 2 matrix. In matrix multiplication the inner product of two vectors is:


And the outer product is:


This is a result of how matrix multiplication is formed by the row by column multiplication.

Well, this has started to look like spam.

*Gets up to get a broom to clean the mess*

If no clear explanations on the posts appear by tomorrow, I will move this to SPAM section

To make this more interesting to people who are just taking geometry here is an example of how matrix multiplication can be used for analytic geometry applications. We can represent a point on a plane as so much to the right, say a to the right and so much to the left, say b to the left of a point called the orgin. The orgin could be the bottom left corner of the paper. Thus the other point is:
[a]
[b]

You can preforme many transformations on this vector for instance you can rotate the point it represents about the orgin by left multiplying the vector by the following rotation matrix
[cos(theta) sin(theta)]
[-sin(theta) cos(theta)]

That is if [c; d] is the point after rotation then:
[c] [cos(theta) sin(theta)][a]
[d]=[-sin(theta) cos(theta)][b]
The matrix:
[cos(theta) sin(theta)]
[-sin(theta) cos(theta)]

Peformes a linear transformation on the vector [a; b]

Pardon me? I spent considerable time writing this. I am not affiliated with any of the sights I linked with hyperlinks. The links were chosen to provide the reader with further information beyond what I have written to help fill in the gaps. Is a discussion of high level math or science forbidden here? Must I always talk to the lowest conman denominator? I tried to proved explanations to my original post because people asked questions about it. Otherwise I could just talk completely over most peoples heads and hope someone with a similar interest joins in.

As far as formatting and such I spent a lot of my time trying to make this post as neat as possible. If there was an alternate text attribute to the image take I could try to replace some of the text by pictures to make it neater. However that would mean my document would not be self contained and if any servers went down the post would make no sense at all. If you could guarantee me web space than I would have a safe place to store my images. However I know the nature here is not to guarantee people web space but rather regiment them to post in a regular pattern following a possibly ridged set of guidelines.

BTW what is the preoccupation here with calling everything spam. Isn’t span just chain mail and unwanted advertising. This certainly isn’t chain mail and what the heck do you think I am advertising????????

are you a math teacher....cuz if ur not...you might want to take up that profession.