Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a certain number of nxn matrices that are positive semidefinite. Is the result of adding all these matrices also positive semidefinite? If affirmative, is it always the case or, instead, in just some instances?

I would also appreciate if you can provide me with the proof or give me a reference I can consult.

Thanks in advance for your help.

share|cite|improve this question

$\rm\bf Observation$: $\hskip 1.5in x^*(A+B)\,x=x^*A\,x+x^*B\,x$

$\rm\bf Rhetorical\;\;Question$: Now what happens if both $x^*A\,x\ge0$ and $x^*B\,x\ge0$?

share|cite|improve this answer
I would recommend using **double asterisks** for bold rather than abusing MathJax's \bf capability. (Similarly, *single asterisks* give you italics.) – Rahul Jan 31 '12 at 6:15

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.