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1.
Using combinatorial arguments we determine the determinantal divisors for the tensor product of two matrices, thereby obtaining its elementary divisors and Jordan canonical form.  相似文献   

2.
We prove that, in a domain of elementary divisors, the intersection of all nontrivial two-sided ideals is equal to zero. We also show that a Bézout domain with finitely many two-sided ideals is a domain of elementary divisors if and only if it is a 2-simple Bézout domain.  相似文献   

3.
We introduce a new class of rings of elementary divisors which generalize adequate rings. We show that the problem of whether every commutative Bezout domain is a domain of elementary divisors reduces to the case where the domain contains only trivial adequate elements (namely, the identities of the domain).  相似文献   

4.
In this paper we give new sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors, which drastically improve and contain some of the previous known conditions. We also show how to perturb complex eigenvalues of a nonnegative matrix while keeping its nonnegativity. These results allow us, under certain conditions, to easily decide if a given list is realizable with prescribed elementary divisors.  相似文献   

5.
Let A(λ) be a monic matrix polynomial. The topological properties (in particular, connectedness) of the set of all right monic divisors of A(λ) with the same determinant are investigated. It turns out that such set of divisors is not connected in general. Sufficient conditions (in terms of the elementary divisors of A(λ)) for its connectedness are provided.  相似文献   

6.
The subring of the Grothendieck ring of k-varieties generated by smooth conics is described, giving many zero divisors. The proof uses only elementary projective geometry.  相似文献   

7.
Let A, B denote the companion matrices of the polynomials xm,xn over a field F of prime order p and let λ,μ be non-zero elements of an extension field K of F. The Jordan form of the tensor product (λI + A)⊗(μI + B) of invertible Jordan matrices over K is determined via an equivalent study of the nilpotent tranformation S of m × n matrices X over F where(X)S = A TX + XB. Using module-theoretic concepts a Jordan basis for S is specified recursively in terms of the representations of m and n in the scale of p, and reduction formulae for the elementary divisors of S are established.  相似文献   

8.
黄礼平 《数学学报》2008,51(2):371-380
设D为除环,A∈Dn×n,则可用初等变换将λI-A化简为对角阵A= diag(1,…,1,φ1,…,φr),其中(?)i为D上首1多项式并且φ1|…|φr.如果这个对角阵A在形状上是唯一的,则称A是有强法式的矩阵.本文应用中心原子因子与初等因子给出了体上有强法式的矩阵的本质刻画,给出了体上矩阵有强法式的一些充要条件.  相似文献   

9.
The concept of an anisotropic vector space with a tensor basis which is invariant under a symmetry transformations of a three-dimensional Euclidean vector space is introduced using the example of symmetric second- and fourth-rank Euclidean tensors. In addition to the traditional operation of summation, the operation of multiplication in a fixed tensor basis is introduced for the elements of this space, that is, the axioms of a ring with an identity element and zero divisors, which enable one to carry out algebraic and functional operations. The possibilities of the proposed mathematical procedure are illustrated using examples of anisotropic tensor functions of a tensor argument, by the general solution of the classical problem of calculating the mean value of the tensor of the moduli of elasticity of a single-phase grain-oriented polycrystalline material and the construction of the strength surfaces of anisotropic composite materials.  相似文献   

10.
We determine the elementary divisors, and hence the rank over an arbitrary field, of the incidence matrix of the classical unital.  相似文献   

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