37 citations · 139 across the 18 of their papers we have counts for
22 papers
Parallels between quaternionic and matrix nullstellensätze
J. Cimprič
We prove a new quaternionic and a new matrix nullstellensatz. We also show that both theories are intertwined.
Local linear dependence of linear partial differential operators
Jaka Cimpric
We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows…
Archimedean classes of matrices over ordered fields
Jaka Cimpric
Let be an ordered field and let be square matrices over of the same size. We say that and belong to the same archimedean class if there exists an intege…
Finsler's Lemma for Matrix Polynomials
Jaka Cimpric
Finsler's Lemma charactrizes all pairs of symmetric real matrices and which satisfy the property that for every nonzero such t…
Real Nullstellensatze and *-ideals in *-algebras
Jakob Cimpric, J. William Helton, Scott McCullough +1
Let F denote either the real or complex field. An ideal I in the free *-algebra F<x,x*> in g freely noncommuting variables and their formal adjoints is a *-ideal if I = I*. When a…
A Real Nullstellensatz for Free Modules
Jaka Cimpric
Let be the algebra of all matrices with entries from $\RR[x_1,\ldots,x_d]$ and let . We will show that for every $a \in \RR^d$ an…