Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose we have two positive definite matrices A and B. Is it correct to claim that all the eigenvalues of A+B are greater or equal to those of A?
Please note that: 1- I need to compare all the eigenvalues and not only the largest ones. 2- A and B are not necessarily diagonal.

share|cite|improve this question

1 Answer 1

up vote 3 down vote accepted

Yes. Weyl's inequality for matrices shows that what you say is true.

share|cite|improve this answer
The Courant minimax principle will work also: – Terry Tao Jul 29 '11 at 5:52
Oh, Terry! You are so kind to answer this one, after your work on A. Horn's conjecture, now Tao-Knutson's theorem. – Denis Serre Jul 29 '11 at 8:41

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.