February 13th, 2017, 04:30 AM  #1 
Newbie Joined: Feb 2017 From: srilanka Posts: 2 Thanks: 0  Positive definiteness
If A is a symmetric positive definite matrix, B is diagonal matrix and B>0 then Can we say AB is positive definite matrix? If so, please let me know the source. Thanks. Last edited by mkayan; February 13th, 2017 at 04:57 AM. 
February 13th, 2017, 02:42 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 642 Thanks: 406 Math Focus: Dynamical systems, analytic function theory, numerics 
definitely not. Take for an example $A = I$ is the identity matrix and $B = 2I$ is twice the identity.

February 13th, 2017, 03:43 PM  #3 
Newbie Joined: Feb 2017 From: srilanka Posts: 2 Thanks: 0 
many thanks.


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definiteness, positive 
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