Math Terms - Visually Described ?

SuperLynx · 2010-12-20 11:54:50

How do you figure how to multiply matrices ?
I know if you want to divide matrices you usually do so in 3D by a vector, but how do you convert a 3x3 matrix to X,Y,Z ?

What is a determent in a 4x4 matrix ?

We also covered XYZ. I told you that unless you are willing to cover the math first 3D graphics will be difficult to understand.
I taught you modulo and clamp and how to rotate and translate points in a cartesian system. I say the same things now that I said then, you have 2 choices.
1) Many graphic programs and languages will create 3D forms for you. They use templates, you do not have to know much math. But you must know the language or the program intimately.
That means experience in using them. You must gain this for yourself, I cannot just hand it to you. You must practice with the commands and the help section that the program provides.
2) The math is also something you learn by experience. You left in the middle of the help, I assume because you thought there was some shortcut way. I hoped you would find it so you could show me this shortcut, I have never found any shortcut way to learn math. I no longer believe there is one.

I understand, I know there is no short-cut but I got more grasp of some of the 3D math that is why I'm resurrecting it again

bobbym · 2010-12-20 12:07:07

do so in 3D by a vector,

You can also divide by a scalar. That still does not mean their is a division of one matrix by another.

How do you figure how to multiply matrices ?

There is formula provided up in post #175. We could work through some of them, but I would start at a 2X2 first.

What is a determent in a 4x4 matrix ?

No one does a 4X4 determinant by hand. Your language will have commands to do these for you. Here is the general answer.

SuperLynx · 2010-12-20 12:31:28

First just lay it out on the table how do you convert a 3x3 matrix to SRT

to

And you forgot about the first set of questions which had "set sum" etc we will go back to matrices but now quite yet

bobbym · 2010-12-20 12:36:18

Hi;

What is SRT?

SuperLynx · 2010-12-20 12:39:41

Scale, Translation & Rotation
(0,0,0) (0,0,0) (0,0,0)

bobbym · 2010-12-20 13:04:20

Hi;

I am not understanding what you are trying to do. What is 345456345?

Is it this?

Are you saying that is 3 points in xyz? Are you using the convention that each column vector is a point?

At present you do not know how to add or multiply 2x2 or 3x3 matrices or a matrix times a vector. You do not yet know how to get the determinant. You do not know how to plot a point in xyz. If I am wrong then let's move on to Wally's page. But if I am right we need to cover the math first.

Cause now we will be working with 4 x 4 matrices and 4 x 1 vectors. That is how they can translate a 3 dimensional point onto a 2 dimensional screen, giving it perspective.

SuperLynx · 2010-12-20 14:38:24

That is what I meant how did you get the forum to write out a Matrix like that ?

Are you saying that is 3 points in xyz? Are you using the convention that each column vector is a point?

Yes that 3 points are in XYZ. As to your second question, I don't understand

At present you do not know how to add or multiply 2x2 or 3x3 matrices or a matrix times a vector. You do not yet know how to get the determinant. You do not know how to plot a point in xyz. If I am wrong then let's move on to Wally's page. But if I am right we need to cover the math first.

I know how to plot a point in XYZ, as for the Matrix math obviously no that is why I resurfaced this thread !

Cause now we will be working with 4 x 4 matrices and 4 x 1 vectors. That is how they can translate a 3 dimensional point onto a 2 dimensional screen, giving it perspective.

Lets begin how to translate then I'm going to show you some math stuff in a image. I can hope you can help me understand something.

bobbym · 2010-12-20 14:45:17

Hi;

bobbym wrote:

Are you using the convention that each column vector is a point?

SuperLynx wrote:

As to your second question, I don't understand

SuperLynx wrote:

as for the Matrix math obviously no

That is my point! How can you go forward? You must learn something about matrices and vectors. You cannot jump to 3D transformations without knowing vector and matrices and the operations on them. That is what does the transformations, matrix operations! You are trying to run without being able to walk yet. You are in China by yourself and cannot speak chinese!

I love your enthusiasm and tenacity but if you do not want to let the program for you, if you want to understand it you must get the basic math. Let me give you that much.

SuperLynx · 2010-12-20 14:58:39

Alright I just want to understand while I put it into practice but begin where you think we shall begin and I'll reply as often as I can throughout.

bobbym · 2010-12-20 15:29:24

This it the 4 x 4 identity matrix. When you multiply any other matrix by this guy nothing happens.

This is for rotations around the x axis.

This is for rotations around the y axis.

This is for rotations around the z axis.

This is for moving or translating an object around. Called the translation matrix.

This called the Scaling matrix. It dilates or shrinks objects.
The numbers on the diagonal are called eigenvalues.

Here is your first view of a matrix transformation of a column vector ( a point on the xyz planes). It is done by matrix times a column vector.

Look at the form of the last one, that tells you how to multiple a 4 x 1 column vector ( the one on the right ) by a 4 x 4 transformation matrix. The above is all you will need, just wanted to show it to you. We will begin with matrix multiplication so that will make sense to you.

First I am going to get something to eat and take a little break.

SuperLynx · 2010-12-21 02:45:18

What I don't understand is the order and what are 5x and 8z represent ?

bobbym · 2010-12-21 09:52:48

Hi SuperLynx;

Is it an algebra problem that you are having? If so we will have cover some of that.

See the column vector.

The x is a variable, in this case it stands for the x coordinate, y is the y coordinate, etc.

The resulting column vector under that transformation is

The first element designated 1,1 ( row 1, column 1 ) is x + 2y + 3z + 4. So if you started with the point ( 3,4,5,1) where 3 is the x coordinate the new x coordinate would be 30

Questions like you are asking strengthen my belief that we will have to cover more matrix operations before you can understand this.
Also I urge you to begin to learn your program and what features it has for matrix multiplication, determinants, etc.

SuperLynx · 2010-12-22 07:15:35

The example you gave I still don't quite understand. I understand what variables are, just so you are away of what I know, and I know the fundamentals of how vectors work, I've already begun working with my 3D programs math and I'm going to post a picture of how it works and the math. In the meantime I want to know how to do the math for a matrix and how to convert a matrix to X,Y,Z.

I know that in 3D matrix each axis has it's own sub-axis so to speak if you want to convert a matrix to these three axis how is that done ?

(0,0,0) = Scale
(0,0,0) = Rotation
(0,0,0) = Movement

bobbym · 2010-12-22 14:29:43

I am not quite understanding what you want. To scale a point:

This is the matrix that scales objects.

This is how a point or a vertices of an object is represented.

To scale the point.

To scale 2 points ( a line for instance )

To scale a triangle ( 3 points )

(0,0,0) = Scale
(0,0,0) = Rotation
(0,0,0) = Movement

I do not know what that is. As far as I understand, scaling, rotating and translating ( moving ) are each done by a separate matrix as I have given them to you in post #185 as S.

SuperLynx · 2010-12-22 15:25:13

I don't understand it the matrix graphs you are displaying how do I read them ? You use terms such as sX Y2 etc.

I do not know what that is. As far as I understand, scaling, rotating and translating ( moving ) are each done by a separate matrix as I have given them to you in post #185 as S.

That is exactly what I want to know is understanding how a matrix is broken into a single row matrix ?

How do I multiply a Matrix by a Vector ? Those are some of the questions I have currently. The way I operate some of these math in the 3D program is similar to MatMat, I'm going to post a screen shot of a simple example to break down how it works, for example subtracting adding two vectors if one is at 1.345 and the other is at 3.456 gives me 4.801 round that off or using another math term gives me 4.8 I just thought of something it would be neat if there was a calculator that would work in conjunction with this type of 3D math, it would be helpful but something I would understand while I learn

bobbym · 2010-12-22 16:09:39

Vector addition is element by element. Each entry inside of a matrix is called an element.

You have it backwards the vector is being multiplied by the matrix. Every matrix is just a collection of vectors. So it is possible to combine 3 points (vectors) into one matrix.

sx is the scaling factor for the x coordiate. Each coordinate is given a name like (x1,y1,z1) is a point in xyz. To plot or transform objects those variables are all replaced by numbers.

Do you have this much down pat.

Please go here and read these. It will not take long.

http://www.mathsisfun.com/algebra/matri … ction.html

http://www.mathsisfun.com/algebra/matri … lying.html

SuperLynx · 2010-12-24 14:03:31

Those two web sites were pretty helpful I have to study these pages more though !

When you multiply a matrix by a matrix that creates a scalar, always ?
Dot Product is where you must always match the first row by the first column, or the second row by the second colunm etc?

Is there a site on how Matrix is converted to a Vector ?

How do you post Matrix in this forum so it shows up as a Matrix ?

Do you have any sites that explain what a 4x4 matrices are ?

Here is a simple tree from my 3D program, I sorta understand but maybe you can help me break it down as to what it's doing ?

The first node from left to right shows the properties, each other node just passes though, most of the time

What I don't understand completely is how a 3x3 matrix works in 3D if each column is X,Y,Z what do the other rows represent ?

bobbym · 2010-12-24 14:26:28

Hi;

You have not covered those two pages yet?

SuperLynx wrote:

Those two web sites were pretty helpful smile I have to study these pages more though !

Nope! Those pages are fundamental! They come first. You have no chance of furthering your understanding without them.

SuperLynx wrote:

When you multiply a matrix by a matrix that creates a scalar, always ?

A matrix times a matrix is never a scalar, it is always a matrix. A scalar in plain english is a single number like 5.

SuperLynx wrote:

Is there a site on how Matrix is converted to a Vector ?

A matrix can be thought of as a bunch of vectors. You do not convert a matrix into a vector.

A matrix x vector = vector.

SuperLynx wrote:

How do you post Matrix in this forum so it shows up as a Matrix ?

You have to use latex to do that.

SuperLynx wrote:

Do you have any sites that explain what a 4x4 matrices are ?

A 4x4 matrix is just a matrix with 4 rows and 4 columns. I have showed you a bunch of them. Nothing special about them.

SuperLynx wrote:

What I don't understand completely is how a 3x3 matrix works in 3D if each column is X,Y,Z what do the other rows represent ?

You are confusing what a program is doing with what math is. All that gui is doing is helping you fill in the boxes of the matrices I showed you in
post # 185.

On the top of the GUI you will see SRT to Matrix, that is bad terminology. That does not mean something is turned into a matrix. When you put in a number in, an element of one of the matrices in post #185 gets it put in the appropriate box.

SuperLynx · 2010-12-24 15:13:28

Nope! Those pages are fundamental! They come first. You have no chance of furthering your understanding without them.

That is why I have to study them further while I put some terms to use while I work !

A matrix times a matrix is never a scalar, it is always a matrix. A scalar in plain english is a single number like 5.

I'm going to have to go over what I read again on this

A matrix can be thought of as a bunch of vectors. You do not convert a matrix into a vector.
A matrix x vector = vector.

I don't understand !

You have to use latex to do that.

???

A 4x4 matrix is just a matrix with 4 rows and 4 columns. I have showed you a bunch of them. Nothing special about them.

I know that a 4x4 is identical to a 3x3, it just has that extra row and I was in a discussion on a 3D graphics forum and the word "determent" always occurs when talking about 4x4 that is what confuses me.

On the top of the GUI you will see SRT to Matrix, that is bad terminology. That does not mean something is turned into a matrix. When you put in a number in, an element of one of the matrices in post #185 gets it put in the appropriate box.

Can you explain or break it down what is happening in the image I posted from the program ?

bobbym · 2010-12-24 15:30:26

I don't understand !

This is a 4 x 4 matrix. It is the scaling matrix.

This is column vector representing a point in the xyz plane. The point is (3,4,5)

Here is how a matrix x vector = vector. The vector on the right is a column vector of 4 x 1.

Latex is a course almost in itself, especially the way I do it. But I can show you maybe an easy way just for matrices.

I will try to decipher what that programmer did with his gui when we come to it. You have much to understand first.

in a discussion on a 3D graphics forum and the word "determent" always occurs when talking about 4x4 that is what confuses me.

You are getting confused over nothing. You can take the determinant of any nxn matrix, not just a 4x4. Please, Oh please do not try to take the determinant of a 4x4 with pencil and paper!

On public tv over here they have several shows with local teachers giving math instruction. You can call in your questions and they will answer them on the air. Well one day a young attractive woman was the teacher for the show. Now, this guy watching the show gets a brilliant idea. He calls in and asks her to find the determinant of a 4x4 with both positive and negative entries. She writes the problem on the board and begins to work on it right there on tv. After all how hard can it be? She can do 2x2 and 3x3's okay so...She struggles and groans with each error. Soon the blackboard is a mess, this is her fourth try and still not the right answer. Our hero, is rolling on the floor, this sadist, this moron, this cretin. Now I do not want you to confuse that imbecile with me, I would never do such a thing.

I am going to a little break now to eat. In the meantime go over those pages. Merry Christmas and a Happy New Year.

SuperLynx · 2010-12-24 17:07:26

In your first example with the 4x4 matrix what does each column and row represent in 3D ?

Latex is a course almost in itself, especially the way I do it. But I can show you maybe an easy way just for matrices.

Please !

I will try to decipher what that programmer did with his gui when we come to it. You have much to understand first.

How much is much ?

You are getting confused over nothing. You can take the determinant of any nxn matrix, not just a 4x4. Please, Oh please do not try to take the determinant of a 4x4 with pencil and paper!

Why should you not try to take the determinant of a 4x4 with a pencil and a paper ?

You can take the determinant of any nxn matrix

I have to still learn why the use of letters is so common in matrices.

On public tv over here they have several shows with local teachers giving math instruction. You can call in your questions and they will answer them on the air. Well one day a young attractive woman was the teacher for the show. Now, this guy watching the show gets a brilliant idea. He calls in and asks her to find the determinant of a 4x4 with both positive and negative entries. She writes the problem on the board and begins to work on it right there on tv. After all how hard can it be? She can do 2x2 and 3x3's okay so...She struggles and groans with each error. Soon the blackboard is a mess, this is her fourth try and still not the right answer. Our hero, is rolling on the floor, this sadist, this moron, this cretin. Now I do not want you to confuse that imbecile with me, I would never do such a thing.

What country is this ? Is the show still on TV ? Was the person asking the question you the end of your paragraph made me wonder but not assume ?

I am going to a little break now to eat. In the meantime go over those pages. Merry Christmas and a Happy New Year.

Same to you, I hope that 2011 brings me much fortune financially as well as starting my freelance career and a attractive women as well, it wouldn't hurt As 2010 and most previous years brought alot of grief, but I learned who brought on this grief as well as what I could have done to change. I can only hope for 2011 it turns around !

bobbym · 2010-12-24 17:38:32

Hi;

I have to still learn why the use of letters is so common in matrices.

That is true in math in general. The use of letters ( variables ) sort of generalizes statements. When I said an n x n matrix you can substitute any positive integer for n, meaning a 3 x 3 ( 3 by 3, 3 rows, 3 columns ) or 4 x 4 or 100 x 100.

Why should you not try to take the determinant of a 4x4 with a pencil and a paper ?

For the same reason you should not try 873654726534 x 8467214253763 in your head, it is beyond most humans. The error she made was in trying that problem to begin with and not understanding someone was sabotaging her.

For latex you can go here, this site uses pull down menus to generate latex.

http://latex.codecogs.com/editor.php

Touch where the picture indicates and more choices will show. Click the one that says \begin{vmatrix}...

A box will come up asking for the size. Enter 3,3 or 4,4 or 2,2 depending on what you want. A template will appear fill it in with the numbers you want. Now you can post that on a forum. When you have done this come back to me and I will show you how to post it here.

SuperLynx · 2010-12-24 18:14:47

That is true in math in general. The use of letters ( variables ) sort of generalizes statements. When I said an n x n matrix you can substitute any positive integer for n, meaning a 3 x 3 ( 3 by 3, 3 rows, 3 columns ) or 4 x 4 or 100 x 100.

Ohh so letters are used as a variable for example which I know sX could be s34, now I know just replace the letters with numbers !

For the same reason you should not try 873654726534 x 8467214253763 in your head, it is beyond most humans. The error she made was in trying that problem to begin with and not understanding someone was sabotaging her.

HaHa I understand !

For latex you can go here, this site uses pull down menus to generate latex.
http://latex.codecogs.com/editor.php
A box will come up asking for the size. Enter 3,3 or 4,4 or 2,2 depending on what you want. A template will appear fill it in with the numbers you want. Now you can post that on a forum. When you have done this come back to me and I will show you how to post it here.
Touch where the picture indicates and more choices will show. Click the one that says \begin{vmatrix}...

I need a legend that explains what each letter means, I don't know where to find /begin ! Why call it a latex editor ?

bobbym · 2010-12-24 18:17:54

The picture in post #197 tells you where to touch with your mouse. Another small box will drop down, touch each one with your mouse and a legend will show up.

You do not have to split the Sx, Sx could be the name of a variable that could equal 23.

SuperLynx · 2010-12-25 02:12:16

bobbym wrote:
The picture in post #197 tells you where to touch with your mouse. Another small box will drop down, touch each one with your mouse and a legend will show up.
When I write in the matrix there are no spaces between the letter like you have ?

You do not have to split the Sx, Sx could be the name of a variable that could equal 23.

What I meant was if you were to read it as a Matrix for each axis that is why I asked if you could lay it out in 3D terms in a matrix formation ?

Math Is Fun Forum

#176 2010-12-20 11:54:50

Re: Math Terms - Visually Described ?

#177 2010-12-20 12:07:07

Re: Math Terms - Visually Described ?

#178 2010-12-20 12:31:28

Re: Math Terms - Visually Described ?

#179 2010-12-20 12:36:18

Re: Math Terms - Visually Described ?

#180 2010-12-20 12:39:41

Re: Math Terms - Visually Described ?

#181 2010-12-20 13:04:20

Re: Math Terms - Visually Described ?

#182 2010-12-20 14:38:24

Re: Math Terms - Visually Described ?

#183 2010-12-20 14:45:17

Re: Math Terms - Visually Described ?

#184 2010-12-20 14:58:39

Re: Math Terms - Visually Described ?

#185 2010-12-20 15:29:24

Re: Math Terms - Visually Described ?

#186 2010-12-21 02:45:18

Re: Math Terms - Visually Described ?

#187 2010-12-21 09:52:48

Re: Math Terms - Visually Described ?

#188 2010-12-22 07:15:35

Re: Math Terms - Visually Described ?

#189 2010-12-22 14:29:43

Re: Math Terms - Visually Described ?

#190 2010-12-22 15:25:13

Re: Math Terms - Visually Described ?

#191 2010-12-22 16:09:39

Re: Math Terms - Visually Described ?

#192 2010-12-24 14:03:31

Re: Math Terms - Visually Described ?

#193 2010-12-24 14:26:28

Re: Math Terms - Visually Described ?

#194 2010-12-24 15:13:28

Re: Math Terms - Visually Described ?

#195 2010-12-24 15:30:26

Re: Math Terms - Visually Described ?

#196 2010-12-24 17:07:26

Re: Math Terms - Visually Described ?

#197 2010-12-24 17:38:32

Re: Math Terms - Visually Described ?

#198 2010-12-24 18:14:47

Re: Math Terms - Visually Described ?

#199 2010-12-24 18:17:54

Re: Math Terms - Visually Described ?

#200 2010-12-25 02:12:16

Re: Math Terms - Visually Described ?

Board footer