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On the construction of Q-controllable graphs
No full textA connected graph is called Q-controllable if its signless Laplacian eigenvalues are mutually distinct and main. Two graphs G and H are said to be Q-cospectral if they share the same signless Laplacian spectrum. In this paper, infinite families of Q-controllable graphs are constructed, by using the operator of rooted product introduced by Godsil and McKay. In the process, innitely many non-isomorphic Q-cospectral graphs are also constructed, especially, including those graphs whose signless Laplacian eigenvalues are mutually distinct
ON ONE-SIDED (B;C)-INVERSES OF ARBITRARY MATRICES
No full textIn this article, one-sided -inverses of arbitrary matrices as well as one-sided inverses along a (not necessarily square) matrix, will be studied. In addition, the -inverse and the inverse along an element will be also researched in the context of rectangular matrices
Low Rank Perturbations of Quaternion Matrices
No full textLow rank perturbations of right eigenvalues of quaternion matrices are considered. For real and complex matrices it is well known that under a generic rank- perturbation the largest Jordan blocks of a given eigenvalue will disappear while additional smaller Jordan blocks will remain. In this paper, it is shown that the same is true for real eigenvalues of quaternion matrices, but for complex nonreal eigenvalues the situation is different: not only the largest , but the largest Jordan blocks of a given eigenvalue will disappear under generic quaternion perturbations of rank . Special emphasis is also given to Hermitian and skew-Hermitian quaternion matrices and generic low rank perturbations that are structure-preserving
Williams, Joan (2017) White Working Class: Overcoming Class Cluelessness in America, Harvard Business Review Press, Boston, Ma.
No full textOrthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
No full textFractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement. An r-fold version of the traditional definition of minimum positive semidefinite rank of a graph using Hermitian matrices that fit the graph is also presented. This paper also introduces r-fold orthogonal representations of graphs and formalizes the understanding of projective rank as fractional orthogonal rank. Connections of these concepts to quantum theory, including Tsirelson's problem, are discussed
Singular Value and Norm Inequalities Associated with 2 x 2 Positive Semidefinite Block Matrices
No full textThis paper aims to give singular value and norm inequalities associated with positive semidefinite block matrices
A transformation that preserves principal minors of skew-symmetric matrices
No full textIt is well known that two symmetric matrices have equal corresponding principal minors of all orders if and only if they are diagonally similar. This result cannot be extended to arbitrary matrices. The aim of this work is to give a new transformation that preserves principal minors of skew-symmetric matrices
Computation of State Reachable Points of Second Order Linear Time-Invariant Descriptor Systems
No full textThis paper considers the problem of computing the state reachable points (from the origin) of a linear constant coefficient second order descriptor system. A new method is proposed to compute the reachable set in a numerically stable way. The original descriptor system is transformed into a strangeness-free system within the behavioral framework followed by a projection that separates the system into different order differential and algebraic equations while keeping the original state variables. This reformulation is followed by a first order formulation that avoids all unnecessary smoothness requirements. For the resulting first order system, it is shown that the computation of the image space of two matrices, associated with the projected system, is enough to numerically compute the reachable set. Moreover, a characterization is presented of all the inputs by which one can reach an arbitrary point in the reachable set. These results are used to compute two different types of reachable sets for second order systems. The new approach is demonstrated through a numerical example
Groups of Matrices That Act Monopotently
No full textIn the present article, the authors continue the line of inquiry started by Cigler and Jerman, who studied the separation of eigenvalues of a matrix under an action of a matrix group. The authors consider groups \Fam{G} of matrices of the form , where is a complex number, and the matrices form an irreducible subgroup of \GL(\C). When \Fam{G} is not essentially finite, the authors prove that for each invertible the set \Fam{G}A contains a matrix with more than one eigenvalue. The authors also consider groups \Fam{G} of matrices of the form , where the matrices comprise a bounded irreducible subgroup of \GL(\C). When \Fam{G} is not finite, the authors prove that for each invertible the set \Fam{G}A contains a matrix with more than one eigenvalue
The Emotional Politics of Making America Great Again: Trump’s Working Class Appeals
No full textReal estate developer and reality TV star Donald Trump’s election to the presidency of the U.S. was a departure from politics as usual in many ways. Most notably, Trump received more white working-class support than any Republican presidential candidate since 1980. Using data from 44 Trump campaign rallies, we analyze Trump’s emotional messages encoded in his working class appeals. We find that Trump’s language (1) temporarily oriented audiences towards feeling shame or fear as a nation, (2) reoriented them towards feeling anger at the elites he blamed, and (3) ultimately promised they would feel safe and proud if he was elected. Trump’s emotional scripting seemed crafted to resonate with working class audiences feeling left behind from decades of bipartisan neoliberalism. We conclude by discussing limitations and potential avenues for future research