12 citations · 16 across the 9 of their papers we have counts for
12 papers
2-step ideals and commuting matrices
Klemen Šivic
2-step ideals are ideals of the polynomial ring that satisfy where is the maximal ideal generated by va…
Cross-positive linear maps, positive polynomials and sums of squares
Igor Klep, Klemen Šivic, Aljaž Zalar
A linear map between matrix spaces is called cross-positive if it is positive on orthogonal pairs of positive semidefinite matrices in the sense that $\langle U,V\rangl…
Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size
Duško Bogdanić, Alen Đurić, Sara Koljančić +2
In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix consisting of two Jordan block…
The solution of the Loewy-Radwan conjecture
Matjaž Omladič, Klemen Šivic
A seminal result of Gerstenhaber gives the maximal dimension of a linear space of nilpotent matrices. It also exhibits the structure of this space where the maximal dimension is at…
On approximate commutativity of spaces of matrices
Matjaž Omladič, Heydar Radjavi, Klemen Šivic
The maximal dimension of commutative subspaces of is known. So is the structure of such a subspace when the maximal dimension is achieved. We consider extensions…
Components and singularities of Quot schemes and varieties of commuting matrices
Joachim Jelisiejew, Klemen Šivic
We investigate the variety of commuting matrices. We classify its components for any number of matrices of size at most 7. We prove that starting from quadruples of size 8 matrices…
Higher-distance commuting varieties
Madeleine Elyze, Alexander Guterman, Ralph Morrison +1
The commuting variety of matrices over a given field is a well-studied object in linear algebra and algebraic geometry. As a set, it consists of all pairs of square matrices with e…
New examples of extremal positive linear maps
Anita Buckley, Klemen Šivic
New families of nonnegative biquadratic forms that have 8, 9 or 10 real zeros in are constructed. These are the first examples with 8, 9 or 10 rea…
There are many more positive maps than completely positive maps
Igor Klep, Scott McCullough, Klemen Šivic +1
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are…
Exotic one-parameter semigroups of endomorphisms of a symmetric cone
Bojan Kuzma, Matjaž Omladič, Klemen Šivic +1
We construct an exotic one-parameter semigroup of endomorphims of a symmetric cone , whose generator is not the sum of a Lie group generator and an endomorphism of . The ques…
On the positive commutator in the radical
Marko Kandić, Klemen Šivic
In this paper we prove that a positive commutator between a positive compact operator and a positive operator is in the radical of the Banach algebra generated by and $…
On varieties of commuting nilpotent matrices
Nham V. Ngo, Klemen Šivic
Let be the variety of all -tuples of commuting nilpotent matrices. It is well-known that is irreducible if , if or if and …