yeah, that''s the article, thanks. I just inverted the words. it explains how to use matrices (vectors are just a specific type of matrix) to do all sorts of nifty physics stuff, I never finished reading it, but it looked promising.

GeekMan Games

heh, and I couldn''t make simple board code work, now who''s the idiot? oh, by the way, the word is "determinant" news to me, I''d never seen it in print before.

My Intro to Lin Alg. book says at the last turn of the century there was a 4 volume book covering the essentials of
determinant applications.
So I imagine that there is some use for them, even if they are a bear to compute.


Bugle4d

That''s crazy... I wonder how people spend a lifetime studying this stuff... I''m trying to be all over programming but just studying determinates??? wow... and then writing a 4 volume set? That''s insane.

-Lewis [m80]
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The determinant analogous to the "volume" of the matrix. If two columns are colinear, the volume of the matrix collapses to zero--obvious in 3 dimensions, also works in N dimensions but hard to picture. The larger the determinant, the more perpendicular the column spaces are from each other.

I only just learned this last year (graduate coursework in digital signal processing), but found it extremely profound--I wonder why it's not more common knowledge? Just about everybody learns the dot product is analogous to projection right off the bat. I guess it's because you have to know about column space to understand this.

[edited by - Stoffel on December 30, 2002 3:42:28 PM]

Thats a interesting statement.
...More perpendicular...
I''ve taken a intro to linear algebra class where we covered column space.

Could you shoot me a explanation of that please ?
I''m not understanding it.

A = |a b|
|c d|
Because if you have det A = (ad-bc)
If you have 2 points defining a rectangle(opposite corners I guess)

Letting the points be the columns that means
|a| |b|
|c|,|d|

And you are doing a mul of the X1 by the Y2, and I just dont get it.

Bugle4d

Lets say you have a 2x2 matrix and the magnitude of each column vector is 1. Maximize the determinant.

[edited by - Stoffel on December 30, 2002 6:15:43 PM]

Let me follow that up by saying that it''s not just how orthogonal the columns are to each other, but really the volume--it''s just easier to get high volume with low magnitude vectors if they''re orthogonal. So it''s not strictly a measurement of the angles between the column space axes.

Hm, I think I''m muddying the issue. I should have just said it''s a measure of the volume of the matrix and left it at that.

Gotcha !

Bugle4d

I''m thinking of adding that fact to my article actually... Do you really think it would make a noticable impression if I did? ( I don''t want to bother Dave in adding to the article if it''s not really worth it )... Alternatively I could just pop it in another article and put other stuff in there aswell... Opinions?

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