How does a matrix indicate a point?

[mynameinc]

I've been looking at the Birkhoff-von Neumann polytope, and the book stated that the vertices are given by the permutation matrices. So, can someone explain how matrices indicate a point in space?

Thanks,

mynameinc

 

[D H]

The vertices are points in ℝ^N2 space.

 

[mynameinc]

The vertices are points in ℝ^N2 space.

I still don't understand. It says that (1 0//0 1), (0 1//1 0) are elements of B_2. How do those indicate points?

If you can't tell, I have several "For Dummies" books. :)

 

[D H]

A 2x2 matrix has four elements, in this case, four real numbers. That maps to R⁴, so they are represented by points in 4-space.

 

[mynameinc]

A 2x2 matrix has four elements, in this case, four real numbers. That maps to R⁴, so they are represented by points in 4-space.

So, does this map as (1,0,1,0) and (0,1,0,1)?

Also, thanks for the help.

 

[Office_Shredder]

Usually if you have a matrix you just read it off from left to right, top to bottom. So the matrix

1 0
0 1

would be (1,0,0,1) and the matrix

0 1
1 0

would be (0,1,1,0). Of course it doesn't matter which order you put the entries of your matrix as long as you're consistent the whole time

 

[mynameinc]

Usually if you have a matrix you just read it off from left to right, top to bottom. So the matrix

1 0
0 1

would be (1,0,0,1) and the matrix

0 1
1 0

would be (0,1,1,0). Of course it doesn't matter which order you put the entries of your matrix as long as you're consistent the whole time

Those are the coordinates I meant to give, lol.

Thanks for the help DH and Office Shredder. Now that I understand, do I need to place [SOLVED] or anything in the title line?