Math Terms - Visually Described ?

bobbym · 2011-01-21 17:06:00

Yes, I can normalize a vector but what did you need it for?

SuperLynx · 2011-01-22 08:08:10

What does Normalize do ?

What are 4x4 matrices, and I assume their is determinants within a 4x4 correct ?

bobbym · 2011-01-22 08:13:40

Normalizing a vector means turning it into a vector with the same direction but a length of 1.

A 4x4 matrix is a matrix with 4 rows and 4 columns. So it has 16 elements.

It is always possible to take the determinant of any square matrix. It is computationally difficult by the standard human methods.

SuperLynx · 2011-01-22 11:17:53

How do you figure out a determinant ???
Normalizing a vectors just means make it always a length of 1 ?

bobbym · 2011-01-22 11:29:42

That is all it means. Its magnitude is 1 yes.

What size are you after? As I said 2 x 2 easy. 3 x 3 hard. 4 x 4 impossible with pencil and paper. Your programming language is similar to Matlab you said. Surely, you have command for it.

SuperLynx · 2011-01-22 11:50:49

How do I figure out the determinant for a 3x3 what do the extra rows & columns in 4x4 represent?

bobbym · 2011-01-22 12:05:58

Hi SuperLynx;

That would depend. In 3D work they use a 4 x 4 for convenience I think. Mathematically only a 3 x 3 is necessary. This I showed you earlier how to rotate, translate and dilate points on a 2D screen. Anything can go into an n x n matrix.

If you now think you can answer this:

3* y - 12 if I plug in 17 into y.

Then I will show you a formula for a 3 x 3 determinant, okay?

SuperLynx · 2011-01-22 13:26:49

If you now think you can answer this:
3* y - 12 if I plug in 17 into y.
Then I will show you a formula for a 3 x 3 determinant, okay?

39???

bobbym · 2011-01-22 13:33:20

Are you sure?

SuperLynx · 2011-01-22 13:44:14

Yes I'm sure !

bobbym · 2011-01-22 13:51:42

Okay. you asked for it, you get it.

Now you told me you can handle this. That is how the guy on that site is getting the determinant.

Now do you want to see how to get a determinant of a real live matrix? If I give you one can you get it?

Lazernugget · 2011-01-22 13:54:02

Lynx, what exactly are you asking for?

SuperLynx · 2011-01-22 14:05:12

I don't understand how you figured out the determinant ? It appears that you are grabbing random letters in the matrix then doing the formula, I know you're not so what are you doing ?

Now do you want to see how to get a determinant of a real live matrix? If I give you one can you get it?

Yes !

Lynx, what exactly are you asking for?

I'm figuring out advanced math piece by piece ! To relate it to an application I use regularly.

Last edited by SuperLynx (2011-01-22 14:05:56)

bobbym · 2011-01-22 14:08:22

Forget about the derivation. It is not important, I do not know it off hand. It is the formula that counts.

Can you find the determinant?

SuperLynx · 2011-01-22 14:18:02

Is there a rule for finding it ?

bobbym · 2011-01-22 14:22:41

Yes I have given you the rule. So, do you need help on that determinant because all you have to do is plug into the formula on the bottom.

This is the rule:

SuperLynx · 2011-01-22 14:40:34

That is the hard rule that must be always followed ?

gAr · 2011-01-22 15:48:49

Hi SuperLynx,

You can do it by using the recursive definition for determinants.

E.g. consider a 3X3 determinant

That is, you take out the first element of the first row, delete the row and column where it lies, and then compute the determinant of the elements which remain.

Then take out the second element of the first row, prefix a minus sign, delete the row and column where it lies, and then compute the determinant of the elements which remain.

Then take out the third element of the first row, prefix a plus sign, delete the row and column where it lies, and then compute the determinant of the elements which remain.

Utimately, we end up in 2X2 determinant, which is easy to compute.
If there are more rows and columns, you compute it in the same way, with alternate plus and minus.

Go here to know some theorems and examples: http://www.numbertheory.org/book/cha4.pdf

Last edited by gAr (2011-01-22 15:51:45)

SuperLynx · 2011-01-22 17:11:24

I'm not following... !

bobbym · 2011-01-22 17:13:05

He just showed you how to do it using minors but you do not know how to do a 2 x 2 so you are stuck using the formula. The rule as you call it.

gAr · 2011-01-22 17:27:27

Hi SuperLynx,

Did you check the document : http://www.numbertheory.org/book/cha4.pdf
I don't know to explain better
Tell what you did not follow.

SuperLynx · 2011-01-23 04:28:23

This is the rule that must always be followed, gAR could you break down the minors.

Correct using the rule I quoted ?

This is for a 3x3 matrix, correct ?

Howardroark · 2011-01-23 05:07:06

Hi Superlynx,

What you've done is wrong.. It's not putting numbers together rather its multiplication..

1x5x9-1x6x8-2x4x9+2x6x7+3x4x8-3x5x7.. and the answer is zero..

SuperLynx · 2011-01-23 05:19:20

?

gAr · 2011-01-23 05:43:34

Hi SuperLynx,

Did you follow?

Math Is Fun Forum

#251 2011-01-21 17:06:00

Re: Math Terms - Visually Described ?

#252 2011-01-22 08:08:10

Re: Math Terms - Visually Described ?

#253 2011-01-22 08:13:40

Re: Math Terms - Visually Described ?

#254 2011-01-22 11:17:53

Re: Math Terms - Visually Described ?

#255 2011-01-22 11:29:42

Re: Math Terms - Visually Described ?

#256 2011-01-22 11:50:49

Re: Math Terms - Visually Described ?

#257 2011-01-22 12:05:58

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#258 2011-01-22 13:26:49

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#259 2011-01-22 13:33:20

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#260 2011-01-22 13:44:14

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#261 2011-01-22 13:51:42

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#262 2011-01-22 13:54:02

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#263 2011-01-22 14:05:12

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#264 2011-01-22 14:08:22

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#265 2011-01-22 14:18:02

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#266 2011-01-22 14:22:41

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#267 2011-01-22 14:40:34

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#268 2011-01-22 15:48:49

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#269 2011-01-22 17:11:24

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#270 2011-01-22 17:13:05

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#271 2011-01-22 17:27:27

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#272 2011-01-23 04:28:23

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#273 2011-01-23 05:07:06

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#274 2011-01-23 05:19:20

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#275 2011-01-23 05:43:34

Re: Math Terms - Visually Described ?

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