Darwinbots Forum

General => Off Topic => Topic started by: Ulciscor on October 06, 2005, 04:24:43 PM

Title: Slightly confused
Post by: Ulciscor on October 06, 2005, 04:24:43 PM

Can anyone give me a hand with this quetion I've been set? I can't seem to work out how to do it.

Think of the points of a plane as being represented by vectors

[y]
Say, in each
                                                                                         
case, whether the set of vectors given is a single point, a line, or the entire plane.


• : [ 1/root(2)   -1/root(2) ]
• = [ 0  0 ][y]   [ 1/root(2)     1/root(2)] [y]     [ 0  0 ]

Title: Slightly confused
Post by: Numsgil on October 06, 2005, 04:28:10 PM

I'm not sure I understand the problem entirely.  In what case would two points represent the entire plane?  Or are we not necessarily talking about two vectors?

Are we talking about R^2?  R^n?  That is, 2D space or ND space?

Title: Slightly confused
Post by: Ulciscor on October 06, 2005, 04:29:43 PM

It just says points of a plane represented by

[y]

It's weird. I think it's something like when you apply a matrix map to a vector you get a known result, so what did the vector you had in the first place represent?

Title: Slightly confused
Post by: Numsgil on October 06, 2005, 05:50:25 PM

Quote

• : [ 1/root(2)   -1/root(2) ]
• = [ 0  0 ][y]   [ 1/root(2)     1/root(2)] [y]     [ 0  0 ]

I'm not sure I understand the notation you're using.  If they're vectors, are we doing vecotr multiplication?  If so, is it dot or cross products?

Title: Slightly confused
Post by: Botsareus on October 06, 2005, 08:47:37 PM

Oxford baby. End of story.

Its a line. looky like y is changing and x is a point, resolting in a vertical line.

Title: Slightly confused
Post by: Ulciscor on October 07, 2005, 08:49:16 AM

:huh:

Title: Slightly confused
Post by: PurpleYouko on October 07, 2005, 09:09:26 AM

Quote

case, whether the set of vectors given is a single point, a line, or the entire plane.

Aren't vectors defined as having a direction? How can vectors represent a point?

Quote

Mathematics

• A quantity, such as velocity, completely specified by a magnitude and a direction.
  
• A one-dimensional array.
  
• An element of a vector space

or are you talking about number 3, a concept which I have very little knowledge of.

Title: Slightly confused
Post by: Botsareus on October 07, 2005, 10:24:25 AM

Quote

Its a line. looky like y is changing and x is a point, resolting in a vertical line.

• : [ 1/root(2) -1/root(2) ]
• = [ 0 0 ][y] [ 1/root(2) 1/root(2)] [y] [ 0 0 ]
  
  In my mind translates to
  
  multi dimentional plain with X having a two dimentional vector were is always (0,0)-( 0,0) because anything - itself = 0
  
  and Y having a two dimentional vector is always ( 1/root(2) ,  1/root(2) ) - (0,0)
  
  resolting in no change along X but a liner along Y. If root(2) is a constant.
  
  Hey what can I say , see if I got it right , thats all.