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Linear maps preserving the Lorentz spectrum: the case
No full textIn this paper, a complete description of the linear maps that preserve the Lorentz spectrum is given when , and is the space of real matrices or the subspace of formed by the symmetric matrices. In both cases, it has been shown that for all , where is a matrix with a certain structure. It was also shown that such preservers do not change the nature of the Lorentz eigenvalues (that is, the fact that they are associated with Lorentz eigenvectors in the interior or on the boundary of the Lorentz cone). These results extend to those for obtained by Bueno, Furtado, and Sivakumar (2021). The case has some specificities, when compared to the case due to the fact that the Lorentz cone in is polyedral, contrary to what happens when it is contained in with Thus, the study of the Lorentz spectrum preservers on also follows from the known description of the Pareto spectrum preservers on
Inverse eigenvalue and related problems for hollow matrices described by graphs
No full textA hollow matrix described by a graph is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in . For a given graph , the determination of all possible spectra of matrices associated with is the hollow inverse eigenvalue problem for . Solutions to the hollow inverse eigenvalue problems for paths and complete bipartite graphs are presented. Results for related subproblems such as possible ordered multiplicity lists, maximum multiplicity of an eigenvalue, and minimum number of distinct eigenvalues are presented for additional families of graphs
A Sylvester-Kac matrix type and the Laplacian controllability of half graphs
No full textIn this paper, we provide a new family of tridiagonal matrices whose eigenvalues are perfect squares. This result motivates the computation of the spectrum of a particular antibidiagonal matrix. As an application, we consider the Laplacian controllability of a particular subclass of chain graphs known as half graphs
The products of involutions in a matrix centralizer
No full textA square matrix is an involution if . The centralizer of a square matrix denoted by is the set of all such that over an algebraically closed field of characteristic not equal to 2. We determine necessary and sufficient conditions for to be a product of involutions in where is a basic Weyr matrix with homogeneous Weyr structure of length 3. Finally, we will show some results for the case when the length of the Weyr structure is greater than 3
Birkhoff-James orthogonality in the trace norm, with applications to quantum resource theories
No full textNumerous results are presented that characterize when a complex Hermitian matrix is Birkhoff-James orthogonal, in the trace norm, to a (Hermitian) positive semidefinite matrix or set of positive semidefinite matrices. For example, a simple-to-test criterion that determines which Hermitian matrices are Birkhoff-James orthogonal, in the trace norm, to the set of all positive semidefinite diagonal matrices is developed. Applications in the theory of quantum resources are explored. For example, the quantum states that have modified trace distance of coherence equal to (the maximal possible value) are characterized, and a connection between the modified trace distance of -entanglement and the NPPT bound entanglement problem is established
Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem
No full textSymplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, have been extended to the case of symplectic eigenvalues. In this note, we will generalize Williamson's diagonal form for symmetric positive-definite matrices to the case of symmetric positive-semidefinite matrices, which allows us to define symplectic eigenvalues, and prove the trace minimization theorem in the new setting
Pascale, C-M, (2021) Living on the Edge: When Hard Times Become a Way of Life. Polity Press.
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How COVID Vaccination Hesitancy, Social Class, and Economic Inequality Reveal a New Dimension of Public Trust
No full textCOVID vaccination data on United States’ citizens reveals that working-class citizens across multicultural domains and political identities are vaccinating at lower rates because working-class citizens do not feel that public institutions have met obligations to improve their life. This belief in unmet obligations illustrates a new facet of institutional trust: a general indifference to institutional requests. This indifference to institutional request, with indifference as a new dimension of trust, differs from past working-class scholarship on institutional trust, which often finds anger, submission, or scapegoating other groups as common responses to institutional request or rhetoric. This article also recapitulates the strong relationship between the U.S.’s high economic inequality and working-class lack of trust and indifference toward public institutions
Editors' Note: Welcome!
No full textWelcome to the Journal of Technology-Integrated Lessons and Teaching (JTILT). This practitioner-focused journal publishes technology-rich lessons and materials for teachers and teacher education audiences around the world. These lessons and materials differ from other repositories because they
are peer-reviewed,
document the design considerations and context associated with instructional development,
include critical reflections regarding implementation,
are freely available for adaptation, use, and dissemination through a Creative Commons, Attribution-Non-commercial-Share-alike 4.0 International license (CC-BY-NC-SA 4.0).
This international journal provides a space to share technology integration approaches in all aspects of the teaching profession (e.g., preservice, induction, inservice, professional development, leadership). Thus, JTILT is a venue to highlight, reflect, and continue conversations regarding teaching approaches. It allows teachers, media specialists, technology coordinators, professors, teacher educators, administrators, and other interested individuals to share best practices and glean from others’ work