Mathematics – Rings and Algebras
Scientific paper
2009-09-08
Mathematics
Rings and Algebras
Scientific paper
It is known that any symmetric matrix $M$ with entries in $\R[x]$ and which is positive semi-definite for any substitution of $x\in\R$, has a Smith normal form whose diagonal coefficients are constant sign polynomials in $\R[x]$. We generalize this result by considering a symmetric matrix $M$ with entries in a formally real principal domain $A$, we assume that $M$ is positive semi-definite for any ordering on $A$ and, under one additionnal hypothesis concerning non-real primes, we show that the Smith normal of $M$ is positive, up to association. Counterexamples are given when this last hypothesis is not satisfied. We give also a partial extension of our results to the case of Dedekind domains.
Quarez Ronan
No associations
LandOfFree
On positive Matrices which have a Positive Smith Normal Form 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 On positive Matrices which have a Positive Smith Normal Form, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On positive Matrices which have a Positive Smith Normal Form will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-108429