Search results for "Diagonal matrices"

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Matrix algebras with degenerate traces and trace identities

2022

In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…

PolynomialAlgebra and Number TheoryTrace (linear algebra)Trace algebrasDiagonal matricesDegenerate energy levelsMathematics - Rings and AlgebrasType (model theory)Polynomial identitiesStirling numbersCombinatoricsMatrix (mathematics)Settore MAT/02 - Algebra16R10 16R30 16R50Rings and Algebras (math.RA)Diagonal matrixFOS: MathematicsDegenerate tracesAlgebra over a fieldCommutative propertyTrace algebras; Polynomial identities; Diagonal matrices; Degenerate traces; Stirling numbersMathematics
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Trace Identities on Diagonal Matrix Algebras

2020

Let Dn be the algebra of n × n diagonal matrices. On such an algebra it is possible to define very many trace functions. The purpose of this paper is to present several results concerning trace identities satisfied by this kind of algebras.

Pure mathematicsTrace (linear algebra)Diagonal matricesCodimensions; Diagonal matrices; Polynomial identities; TracesDiagonal matriceCodimensionsPolynomial identitiesSettore MAT/02 - AlgebraPolynomial identitieCodimensionTracesDiagonal matrixAlgebra over a fieldMathematicsTrace
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