13 citations · 39 across the 25 of their papers we have counts for
9 papers · 1 filter
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…
Cholesky decomposition of positive semidefinite matrices over commutative semirings
David Dolžan, Polona Oblak
We prove that over a commutative semiring every symmetric strongly invertible matrix with nonnegative numerical range has a Cholesky decomposition.
The total zero-divisor graph of commutative rings
Alen Đurić, Sara Jevđenić, Polona Oblak +1
In this paper we initiate the study of the total zero-divisor graphs over commutative rings with unity. These graphs are constructed by both relations that arise from the zero-divi…
Bounds for the completely positive rank of a symmetric matrix over a tropical semiring
David Dolžan, Polona Oblak
In this paper, we find an upper bound for the CP-rank of a matrix over a tropical semiring, according to the vertex clique cover of the graph prescribed by the pattern of the matri…
The total graphs of finite rings
David Dolžan, Polona Oblak
In this paper we extend the study of total graphs to non-commutative finite rings . We prove that is connected if and only if is not local and we see that in t…
On the nilpotent commutator of a nilpotent matrix
Polona Oblak
We study the structure of the nilpotent commutator $\nb$ of a nilpotent matrix . We show that $\nb$ intersects all nilpotent orbits for conjugation if and only if is a squar…
Diameters of commuting graphs of matrices over semirings
David Dolžan, Damjana Kokol Bukovšek, Polona Oblak
We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the…
The zero-divisor graphs of semirings
David Dolžan, Polona Oblak
In this paper we study zero--divisor graphs of rings and semirings. We show that all zero--divisor graphs of (possibly noncommutative) semirings are connected and have diameter les…
On maximal distances in a commuting graph
Gregor Dolinar, Bojan Kuzma, Polona Oblak
We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained onl…