positive definite (1 Viewer)

[tebbybear]

can someone please tell me what the hell is a positive definite?

 

[withoutaface]

a polynomial which is postive whatever the value of x is; x² is an example

 

[acmilan]

Its been a while but i think this is how it goes. Positive definite is when the function is always completely above x-axis (negative is when completely below) and doesnt cut the axis. The equation y = ax² + bx + c is a positive definite if two conditions are true and you can find out if these two conditions are true:
1. a > 0 (for negative definite a < 0)
2. b² - 4ac < 0
That would make y = x² not a positive definite if how i remember it is correct

 

[tebbybear]

hmmm... so to prove if an equation is a positive definite...
i have to prove that the discriminant is < 0

 

[velox]

And that the coefficient of x is positive. Positive definite functions have no roots, and are concave up.

 

[wanton-wonton]

And that the coefficient of x is positive. Positive definite functions have no roots, and are concave up.

no...its the coefficient of x^2, for a quadratic.

 

[nick1048]

Positive definite = the graph is always positive. For every x value there is a corresponding y value above the x-axis

 

[velox]

no...its the coefficient of x^2, for a quadratic.

wtf? What i said is right....... Wanton ur a bit messed up.....

 

[acmilan]

wtf? What i said is right....... Wanton ur a bit messed up.....

Its the coefficient of x² that has to be positive, atleast thats what ive been told. Otherwise the function will be concave down.

 

[Xayma]

a polynomial which is postive whatever the value of x is; x² is an example

But x² isn't positive for x=0, it is just non-negative.

x²+1 is a better example.

 

[withoutaface]

But x² isn't positive for x=0, it is just non-negative.

x²+1 is a better example.

Hahahaha whoops

 

[velox]

Its the coefficient of x² that has to be positive, atleast thats what ive been told. Otherwise the function will be concave down.

oh yeah, thats what i meant, hmmm was a bit late when i posted that

 

[Slidey]

sinx + 2 is perhaps an example of a pos def function which is easier to visualise.

 

[blackbunny]

i got a diagram to make u r life easier

 

[Trev]

sinx + 2 is perhaps an example of a pos def function which is easier to visualise.

how is that easier to visualise than Xayma's "x^2 + 1"? i dont even kno wat sinx looks like heh

 

[Slidey]

If you knew what a sin graph looked like, maybe it WOULD be simpler to visualise!

 

[zenger69]

Everyone who's posted on this forum is right. You've all blow something trivial out of proportion.