Do i have to consider the complex case of triangle inequality

1. Nov 22, 2008

transgalactic

in order for me to understand this theorim
do i have to think of the vectors as complex??

what the values of x1 ,y1 ,x2 ,y2

$$\langle x , y \rangle = x_1^* \cdot y_1 + x_2^*\cdot y_2 + \ldots$$
did i get the structure correctly

x=(x1,y1) y=(y1,y2) each one of x1,x2,y1,y2 is a complex number??

2. Nov 22, 2008

Dick

That has not much to do with any triangle inequality, but yes, it looks like the definition of a complex inner product. And I think your understanding of what the objects are is fine.

3. Nov 22, 2008

transgalactic

i know that the sum of two sides is always bigger then the third one

but in this formula
|x+y|=<|x| +|y|

on both sides i have a sum of two members
why the third side is |x+y| ??
and why there is an option for them to be equal??
(the sum of two sides is always bigger then the third one)

4. Nov 22, 2008

Dick

You are supposed to be thinking of x and y as vectors. If the vector x represents one side and the vector -y represents the other side, x+y represents the third side. The sum of the sides can be equal to the third side if all three vertices lie on the same line.

5. Nov 22, 2008

transgalactic

in the article they present the case where they use it in a simple way of
|x+y|=<|x| +|y|

http://en.wikipedia.org/wiki/Triangle_inequality

if both the sides lie on the third line then its not a triangle(its not legal)

on both sides i have a sum of two members
why the third side is |x+y| ??
and why there is an option for them to be equal??
(the sum of two sides is always bigger then the third one)