Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

Details Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

2005-04-29

arxiv.org/abs/math/0504587v1

Mathematics

Operator Algebras

13 Pages, Novel Approaches to Hard Discrete Optimization, Fields Institute Communications

Scientific paper

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eigenvalues is identified, and considerable evidence is given for the conjecture that no other words do.

Affiliated with

Also associated with

No associations

Rating

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-402680