What is a Convex Hull and How Does it Relate to Positive Definite Objects?

[Tenshou]

I don't understand what a convex hull is and what it does. does anyone think they can explain what exactly it is?

 

[micromass]

The convex hull of A is the smallest convex set that contains A.

If you want to see what it is, then you should experiment. Draw 2 points on a sheet of paper. What do you think that the convex hull is?
What about 3 points?
What about 4 points?

 

[Tenshou]

Thank you micromass, I think I get it... I think I understand that the two points should be a line segment, 3 points a triangle and 4 a tetrahedron. I just don't get why those are convex sets, is it because the dimension of the line segment(or the other stuff) is equal to the dimension of the plane that it sits in? Why isn't a circle a convex hull or a square? are they convex sets?

 

[lavinia]

Thank you micromass, I think I get it... I think I understand that the two points should be a line segment, 3 points a triangle and 4 a tetrahedron. I just don't get why those are convex sets, is it because the dimension of the line segment(or the other stuff) is equal to the dimension of the plane that it sits in? Why isn't a circle a convex hull or a square? are they convex sets?

what is the definition od a convex set?

 

[Tenshou]

I do not know, but I think it talks about some set which is Positive Definite "object", but I am not sure :/ I mean just thinking about convex things that is what I think it could be.