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Grimus, W.; Ecker, G.
Vienna Univ. (Austria). Inst. fuer Theoretische Physik
Vienna Univ. (Austria). Inst. fuer Theoretische Physik
AbstractAbstract
[en] We prove two theorems on the simultaneous diagonalizability of a set of complex square matrices by a biunitary transformation. (Author)
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1986; 4 p
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[en] There are many theorems concerning the eigenvalues of matrices with dominant main diagonal, but very few when this condition is not satisfied. The theorem here proposed belongs to this second category
[fr]
Il existe de nombreux theoremes sur les valeurs propres des matrices a diagonale principale dominante, mais beaucoup moins lorsque cette condition n'est pas remplie, le theoreme propose ici appartient a cette seconde categorieOriginal Title
Sur la valeur propre de plus grande partie reelle dans un certain type de matrices
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C. R., Ser. A; v. 280(14); p. 925-928
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Mahdavi-Hezavehi, M.
International Centre for Theoretical Physics, Trieste (Italy)
International Centre for Theoretical Physics, Trieste (Italy)
AbstractAbstract
[en] Matrix orderings on rings are investigated. It is shown that in the commutative case they are essentially positive cones. This is proved by reducing it to the field case; similarly one can show that on a skew field, matrix positive cones can be reduced to positive cones by using the Dieudonne determinant. Our main result shows that there is a natural bijection between the matrix positive cones on a ring R and the ordered epic R-fields. (author). 7 refs
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Aug 1990; 8 p
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Guterman, A.; Soares, G., E-mail: guterman@list.ru, E-mail: gsoares@utad.pt
AbstractAbstract
[en] Let matrices A,C ∈ Mn have eigenvalues α1, . . ., αn and γ1, . . . , γn, respectively. The set of complex numbers DC(A) = {det(A−UCU*) : U ∈ Mn, U*U = In} is called the C-determinantal range of A. The paper studies various conditions under which the relation DC(R S) = DC(S R) holds for some matrices R and S.
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Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
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Khan, M.A.
International Centre for Theoretical Physics, Trieste (Italy)
International Centre for Theoretical Physics, Trieste (Italy)
AbstractAbstract
[en] We study the commutativity of certain class of rings, namely rings with unity 1 and right s-unital rings under each of the following properties [yxm - xn f(y)xp,x]=0, [yxm+xnf(y)xp,x]=0, where f(t) is a polynomial in t2Z[t] varying with pair of ring elements x,y and m,n,p are fixed non-negative integers. Moreover, the results have been extended to the case when m and n depend on the choice of x and y and the ring satisfies the Chacron's Theorem. (author). 14 refs
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Aug 1994; 5 p
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Vavilov, N. A., E-mail: nikolai-vavilov@yandex.ru
AbstractAbstract
[en] Decomposition of unipotents gives short polynomial expressions of the conjugates of elementary generators as products of elementaries. It turns out that with some minor twist the decomposition of unipotents can be read backwards to give very short polynomial expressions of the elementary generators themselves in terms of elementary conjugates of an arbitrary matrix and its inverse. For absolute elementary subgroups of classical groups this was recently observed by Raimund Preusser. I discuss various generalizations of these results for exceptional groups, specifically those of types E6 and E7, and also mention further possible generalizations and applications.
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Copyright (c) 2019 Springer Science+Business Media, LLC, part of Springer Nature; Country of input: International Atomic Energy Agency (IAEA)
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[en] Positive-definite Hankel matrices have an important property: the ratio of the largest and the smallest eigenvalues (the spectral condition number) has as a lower bound an increasing exponential of the order of the matrix that is independent of the particular matrix entries. The proof of this fact is related to the so-called Vandermonde factorizations of positive-definite Hankel matrices. In this paper the structure of these factorizations is studied for real sign-indefinite strongly regular Hankel matrices. Some generalizations of the estimates of the spectral condition number are suggested
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Available from http://dx.doi.org/10.1070/SM2001v192n04ABEH000557; Country of input: International Atomic Energy Agency (IAEA)
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Sbornik. Mathematics; ISSN 1064-5616;
; v. 192(4); p. 537-550

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Cicuta, Giovanni M; Molinari, Luca Guido, E-mail: giovanni.cicuta@fis.unipr.it, E-mail: luca.molinari@unimi.it
AbstractAbstract
[en] The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries and are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology. (paper)
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Available from http://dx.doi.org/10.1088/1751-8113/49/37/375601; Country of input: International Atomic Energy Agency (IAEA)
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Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 49(37); [16 p.]

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[en] Let A be an n by n matrix which may be singular with a one-dimensional null space, and consider the LU-factorization of A. When A is exactly singular, we show conditions under which a pivoting strategy will produce a zero nth pivot. When A is not singular, we show conditions under which a pivoting strategy will produce an nth pivot that is O(sigma/sub n/) or O(kappa-1(A)), where sigma/sub n/ is the smallest singular value of A and kappa(A) is the condition number of A. These conditions are expressed in terms of the elements of A-1 in general but reduce to conditions on the elements of the singular vectors corresponding to sigma/sub n/ when A is nearly or exactly singular. They can be used to build a 2-pass factorization algorithm which is guaranteed to produce a small nth pivot for nearly singular matrices. As an example, we exhibit an LU-factorization of the n by n upper triangular matrix
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Mathematics of Computation; ISSN 0025-5718;
; v. 42(166); p. 535-547

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Abbasi, S.J.
International Centre for Theoretical Physics, Trieste (Italy)
International Centre for Theoretical Physics, Trieste (Italy)
AbstractAbstract
[en] This paper was motivated by the question: Does, like the ring case, the process of taking Jacobson Radicals and constructing matrix near rings coincide? We present here, for the class of weakly distributive d.g. near rings, a conditionally affirmative answer to this question. Our main result is as follows: Let R be a weakly distributive d.g. near ring with identity. If J(R) is contained δ1Mn(R), the derived group of Mn(R), then J(R)=J(Mn(R)) where I-bar is defined as a subnear ring of Mn(R) generated by {faij; a is an element of I, 1 ≤ i, j ≤ n}. (author). 6 refs
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Jan 1994; 5 p
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