scholarly journals Full column rank preservers that preserve semipositivity of matrices

2018 ◽  
Vol 6 (1) ◽  
pp. 37-45
Author(s):  
Chandrashekaran Arumugasamy ◽  
Sachindranath Jayaraman
Keyword(s):  
Full Column Rank ◽  
Left Invertibility ◽  
Dimension 2

Abstract Left invertibility preservers on Mm,n(ℝ), m ≥ n, that preserve either semipositivity of matrices or the subset of minimally semipositive matrices are studied. We prove that such maps cannot be degenerate. We also highlight the structure of nonsingular subspaces of dimension 2 in M2(ℝ).

scholarly journals Typical ranks of certain 3-tensors and absolutely full column rank tensors

2017 ◽  
Vol 66 (1) ◽  
pp. 193-205 ◽  
Author(s):  
Mitsuhiro Miyazaki ◽  
Toshio Sumi ◽  
Toshio Sakata
Keyword(s):  
Full Column Rank

scholarly journals Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Gradient Descent ◽  
Main Idea ◽  
Full Column Rank ◽  
Minimum Error ◽  
Matrix Coefficients ◽  
Special Cases ◽  
Efficiency And Effectiveness ◽  
Associated Matrix

AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

scholarly journals GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR

2021 ◽  
pp. 1-54
Author(s):  
MANUEL L. REYES ◽  
DANIEL ROGALSKI
Keyword(s):  
Regularity Property ◽  
Graded Algebra ◽  
General Study ◽  
Locally Finite ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Dimension 2 ◽  
Separable Algebras ◽  
Gk Dimension

Abstract This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k-algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension.

scholarly journals Who Gets what and how Does it Matter? Importance-Weighted Portfolio Allocation and Coalition Support in Brazil

2018 ◽  
Vol 10 (3) ◽  
pp. 99-134 ◽  
Author(s):  
Mariana Batista
Keyword(s):  
Positive Relationship ◽  
Portfolio Allocation ◽  
Weighted Portfolio ◽  
Dimension 2 ◽  
Legislative Support ◽  
Presidential Systems

Who gets what in portfolio allocation, and how does it matter to coalition partners’ legislative support in presidential systems? I propose that portfolios are not all alike, and that their allocation as well as the support for the president's agenda depends on the particular distribution of assets within the executive. The portfolio share allocated to coalition parties is weighted by a measure of importance based on the assets controlled by the ministry in question, such as policies, offices, and budgets. Once the weighted allocation of ministries has been identified, the results show that: 1) the president concentrates the most important ministries in their own party, mainly considering the policy dimension; 2) the positive relationship between portfolio allocation and legislative support remains, with the importance of specific dimensions being considered; and, 3) coalition partners do not respond differently in terms of legislative support in light of the different assets’ distribution within the portfolio allocation.

Perceiving Hierarchical Structures in Nonrepresentational Paintings

1998 ◽  
Vol 16 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Tsion Avital ◽  
Gerald C. Cupchik
Keyword(s):  
Factor Analysis ◽  
Multidimensional Scaling ◽  
Hierarchical Structure ◽  
Hierarchical Structures ◽  
Exploratory Activity ◽  
Affective Responses ◽  
Hierarchical Complexity ◽  
The Hierarchical Structure ◽  
Relative Separation ◽  
Dimension 2

A series of four experiments were conducted to examine viewer perceptions of three sets of five nonrepresentational paintings. Increased complexity was embedded in the hierarchical structure of each set by carefully selecting colors and ordering them in each successive painting according to certain rules of transformation which created hierarchies. Experiment 1 supported the hypothesis that subjects would discern the hierarchical complexity underlying the sets of paintings. In Experiment 2 viewers rated the paintings on collative (complexity, disorder) and affective (pleasing, interesting, tension, and power) scales, and a factor analysis revealed that affective ratings were tied to complexity (Factor 1) but not to disorder (Factor 2). In Experiment 3, a measure of exploratory activity (free looking time) was correlated with complexity (Factor 1) but not with disorder (Factor 2). Multidimensional scaling was used in Experiment 4 to examine perceptions of the paintings seen in pairs. Dimension 1 contrasted Soft with Hard-Edged paintings, while Dimension 2 reflected the relative separation of figure from ground in these paintings. Together these results show that untrained viewers can discern hierarchical complexity in paintings and that this quality stimulates affective responses and exploratory activity.

scholarly journals A Note On Umbilics of a Closed Surface

1959 ◽  
Vol 15 ◽  
pp. 219-223
Author(s):  
Minoru Kurita
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Closed Surface ◽  
Dimension 2 ◽  
Direction Field

In this paper we investigate indices of umbilics of a closed surface in the euclidean space. Most part of the discussion is concerned with a symmetric tensor field of degree 2, or rather a direction field, on a Riemannian manifold of dimension 2.

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