Do i have to consider the complex case of triangle inequality

[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??

 

[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.

 

[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)

 

[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.

 

[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)