Results 21 to 30 of about 55 (55)

Completely positive matrices over Boolean algebras and their CP-rank

Special Matrices, 2015
Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite ...
Mohindru Preeti
doaj   +1 more source

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion ...
Kösal Hidayet Hüda, Akyiğit Mahmut, Tosun Murat   +2 more
doaj   +1 more source

Idempotents which are products of two nilpotents

Special Matrices
Over any GCD (greatest common divisor) commutative domain we show that the nontrivial 2×22\times 2 idempotent matrices are products of two nilpotent matrices. In order to find explicitly such decompositions, two procedures are described.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion ...
Kosal Hidayet Huda, Tosun Murat
doaj   +1 more source

From lattices to Hv-matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices.
Křehlík Štěpán, Novák Michal
doaj   +1 more source

Diagonal operators, \(q\)-Whittaker functions and rook theory

We discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field \(\mathbb{F}_q\).
Ram, Samrith, Schlosser, Michael J.
core   +1 more source

Subspace profiles over finite fields and q-Whittaker expansions of symmetric functions

Forum of Mathematics, Sigma
Bender, Coley, Robbins, and Rumsey posed the problem of counting the number of subspaces which have a given profile with respect to a linear endomorphism defined on a finite vector space.
Samrith Ram
doaj   +1 more source

Jordan left derivations in infinite matrix rings

Demonstratio Mathematica
Let RR be a unital associative ring. Our motivation is to prove that left derivations in column finite matrix rings over RR are equal to zero and demonstrate that a left derivation d:T→Td:{\mathcal{T}}\to {\mathcal{T}} in the infinite upper triangular ...
Zhang Daochang, Ma Leiming, Hu Jianping, Sun Chaochao   +3 more
doaj   +1 more source

The perturbation of Drazin inverse and dual Drazin inverse

Special Matrices
In this study, we derive the Drazin inverse (A+εB)D{\left(A+\varepsilon B)}^{D} of the complex matrix A+εBA+\varepsilon B with Ind(A+εB)>1{\rm{Ind}}\left(A+\varepsilon B)\gt 1 and Ind(A)=k{\rm{Ind}}\left(A)=k and the group inverse (A+εB)#{\left(A ...
Wang Hongxing, Cui Chong, Wei Yimin
doaj   +1 more source

Determinants of tridiagonal matrices over some commutative finite chain rings

Special Matrices
Diagonal matrices and their generalization in terms of tridiagonal matrices have been of interest due to their nice algebraic properties and wide applications.
Jitman Somphong, Sricharoen Yosita
doaj   +1 more source