In term of symmetric matrices

Being Positive definite is equivalent to the condition that all the eigenvalues of the matrix are positive.

Being non positive definite is just the opposite, i.e., at least one of the eigenvalues is non-positive.

所有跟帖： 

• 学习了, 多谢! -flagsix- ♂ (0 bytes) () 03/06/2015 postreply 18:09:07

• The opposite of positve is negative. Non-positve symmetric -weston- ♀ (160 bytes) () 03/06/2015 postreply 18:15:59

• It's only wrong b/c you missed the context. -weston- ♀ (0 bytes) () 03/06/2015 postreply 21:23:03

• Your old defense trick again! :) -career- ♂ (0 bytes) () 03/06/2015 postreply 21:27:41

• You are as right here as your "sinc(x) is NND". What a joke. -weston- ♀ (0 bytes) () 03/07/2015 postreply 06:10:39

• Yes, sinc(x) is non-negative definite, because its Fourier Tran -career- ♂ (212 bytes) () 03/07/2015 postreply 06:42:57

• Bochner calls it "positive definite", not "NND". Get a better te -weston- ♀ (0 bytes) () 03/07/2015 postreply 06:56:21

• FT(sinc(x)) becomes zero at lots of points, doesn't it? -career- ♂ (53 bytes) () 03/07/2015 postreply 07:06:36

• Sigh. You don't understand the proof of the Bochner Theorem. Go -weston- ♀ (0 bytes) () 03/07/2015 postreply 09:05:12

• You don't need more "proof"--it's by the definition! :) -career- ♂ (0 bytes) () 03/07/2015 postreply 09:15:36

• Surprised anyway would hire someone like you who doesn't know -weston- ♀ (78 bytes) () 03/07/2015 postreply 09:44:02

• You forgot any integral over a zero-valued set yields zero. :) -career- ♂ (62 bytes) () 03/07/2015 postreply 11:18:28

• Your step function is not zero over an open interval. Check Four -weston- ♀ (0 bytes) () 03/07/2015 postreply 11:21:46

• It's a rectangular function--not a "step"! -career- ♂ (67 bytes) () 03/07/2015 postreply 11:33:18

• Wikipedia "rectangular function, the next simplest step function -weston- ♀ (0 bytes) () 03/07/2015 postreply 11:40:53

• hoho, you even need Wiki for that! :) -career- ♂ (168 bytes) () 03/07/2015 postreply 11:46:47

• For your conenience only, since you had idea step functions cove -weston- ♀ (0 bytes) () 03/07/2015 postreply 11:57:00

• I have the rectangular. it is you who "mis"-"step":))) -career- ♂ (567 bytes) () 03/07/2015 postreply 11:59:34

• 你这是 "白马非马" 的现代版 -weston- ♀ (0 bytes) () 03/07/2015 postreply 12:03:16

• Stay in math,pls. :) -career- ♂ (0 bytes) () 03/07/2015 postreply 12:19:30

• :( -career- ♂ (38 bytes) () 03/06/2015 postreply 20:38:52

• was already said -weston- ♀ (0 bytes) () 03/06/2015 postreply 21:24:44

• This? :) -career- ♂ (677 bytes) () 03/06/2015 postreply 21:47:52