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Relevant bibliographies by topics / Determinantal

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Journal articles

Academic literature on the topic 'Determinantal'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Determinantal"

1

Dey, Papri. "Definite determinantal representations of multivariate polynomials." Journal of Algebra and Its Applications 19, no. 07 (2019): 2050129. http://dx.doi.org/10.1142/s0219498820501297.

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In this paper, we consider the problem of representing a multivariate polynomial as the determinant of a definite (monic) symmetric/Hermitian linear matrix polynomial (LMP). Such a polynomial is known as determinantal polynomial. Determinantal polynomials can characterize the feasible sets of semidefinite programming (SDP) problems that motivates us to deal with this problem. We introduce the notion of generalized mixed discriminant (GMD) of matrices which translates the determinantal representation problem into computing a point of a real variety of a specified ideal. We develop an algorithm to determine such a determinantal representation of a bivariate polynomial of degree [Formula: see text]. Then we propose a heuristic method to obtain a monic symmetric determinantal representation (MSDR) of a multivariate polynomial of degree [Formula: see text].

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2

Kyrchei, Ivan I. "Determinantal Representations of the Core Inverse and Its Generalizations with Applications." Journal of Mathematics 2019 (October 1, 2019): 1–13. http://dx.doi.org/10.1155/2019/1631979.

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In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

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3

Marcus, Marvin. "Determinantal Loci." College Mathematics Journal 23, no. 1 (1992): 44. http://dx.doi.org/10.2307/2686198.

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4

Fulton, William. "determinantal formulas." Duke Mathematical Journal 65, no. 3 (1992): 381–420. http://dx.doi.org/10.1215/s0012-7094-92-06516-1.

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5

Beauville, Arnaud. "Determinantal hypersurfaces." Michigan Mathematical Journal 48, no. 1 (2000): 39–64. http://dx.doi.org/10.1307/mmj/1030132707.

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6

Marcus, Marvin. "Determinantal Loci." College Mathematics Journal 23, no. 1 (1992): 44–47. http://dx.doi.org/10.1080/07468342.1992.11973433.

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7

Kimura, Kenichiro, Shun-ichi Kimura, and Nobuyoshi Takahashi. "Motivic zeta functions in additive monoidal categories." Journal of K-theory 9, no. 3 (2011): 459–73. http://dx.doi.org/10.1017/is011011006jkt174.

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AbstractLet C be a pseudo-abelian symmetric monoidal category, and X a Schur-finite object of C. We study the problem of rationality of the motivic zeta function ζx(t) of X. Since the coefficient ring is not a field, there are several variants of rationality — uniform, global, determinantal and pointwise rationality. We show that ζx(t) is determinantally rational, and we give an example of C and X for which the motivic zeta function is not uniformly rational.

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8

Stanimirović, Predrag S., and Milan Lj Zlatanović. "Determinantal Representation of Outer Inverses in Riemannian Space." Algebra Colloquium 19, spec01 (2012): 877–92. http://dx.doi.org/10.1142/s1005386712000740.

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Starting from a known determinantal representation of outer inverses, we derive their determinantal representation in terms of the inner product in the Euclidean space. We define the double inner product of two miscellaneous tensors of rank 2 in a Riemannian space. The corresponding determinantal representation as well as the general representation of outer inverses in the Riemannian space are derived. A non-zero {2}-inverse X of a given tensor A obeying ρ(X) = s with 1 ≤ s ≤ r = ρ(A) is expressed in terms of the double inner product involving compound tensors with minors of order s, extracted from A and appropriate tensors.

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9

Conca, Aldo. "Symmetric ladders." Nagoya Mathematical Journal 136 (December 1994): 35–56. http://dx.doi.org/10.1017/s0027763000024958.

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In this paper we define and study ladder determinantal rings of a symmetric matrix of indeterminates. We show that they are Cohen-Macaulay domains. We give a combinatorial characterization of their h-vectors and we compute the a-invariant of the classical determinantal rings of a symmetric matrix of indeterminates.

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10

Hardy, Adrien, and Mylène Maïda. "Determinantal Point Processes." EMS Newsletter 2019-6, no. 112 (2019): 8–15. http://dx.doi.org/10.4171/news/112/3.

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