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Schennum, Jill (2023) As Goes Bethlehem: Steelworkers and the Restructuring of an Industrial Working Class. Vanderbilt University Press
No full text“Learning in the Dark” Simulation to Teach about Accessibility
No full textThe purpose of this instructor-led lesson is to raise preservice teachers’ awareness of the significance of accessibility in PK-12 education. In the lesson, students develop empathy to understand the experiences of learners with vision-related disabilities through a simulation activity and competencies to achieve accessibility in their specific teaching contexts. Multimedia and open educational resources are utilized to introduce accessibility, inclusive education, Universal Design for Learning, assistive technology, and accessibility evaluation. Students participate in several learning activities, such as a collaborative document to identify effective technologies to address accessibility issues faced by learners with disabilities and an e-portfolio assessment to evaluate the accessibility of e-learning tools in PK-12 classrooms
Centered PSD matrices with thin spectrum are M-matrices
No full textWe show that real, symmetric, centered (zero row sum) positive semidefinite matrices of order and rank with eigenvalue ratio between the largest and smallest nonzero eigenvalue have nonpositive off-diagonal entries, and that this eigenvalue criterion is tight. The result is relevant in the context of matrix theory and inverse eigenvalue problems, and we discuss an application to Laplacian matrices
Linear maps that preserve parts of the spectrum on pairs of similar matrices
No full textIn this paper, we characterize linear bijective maps on the space of all matrices over an algebraically closed field having the property that the spectrum of and have at least one common eigenvalue for each similar matrices and . Using this result, we characterize linear bijective maps having the property that the spectrum of and have common elements for each matrices and having the same spectrum. As a corollary, we also characterize linear bijective maps preserving the equality of the spectrum
The matrix inverse Young inequality
No full textAn inverse Young inequality is established for positive definite matrices
Eigenvalues for stochastic matrices with a prescribed stationary distribution
No full textGiven a vector 0<w \in \mathbb{R}^n whose entries sum to , the region in the complex plane consisting of all eigenvalues of all stochastic matrices having as a left Perron vector is considered. Some general observations about this region are made, it is proven that \bigcap_{w \in \mathbb{R}^n, w>0, w^\top \mathbf{1} =1} \sigma_\mathcal{S}(w) =[0,1], and a characterization is given of the vectors such that contains an element with The corresponding problem for reversible stochastic matrices with given left Perron vector is also considered, as is the corresponding region which is a subset of Under a mild hypothesis on it is proven that the smallest element of corresponds to a reversible stochastic matrix whose graph is a tree with a loop at one vertex. A general lower bound on the eigenvalues of reversible stochastic matrices with given left Perron vector is also given, as is a complete description of when has two or three entries
Expressions and characterizations for the Moore-Penrose inverse of operators and matrices
No full textUnder certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its computation. We give formulations of them for finite matrices and study the Moore-Penrose inverse of circulant matrices and of distance matrices of certain graphs
On the sum of the k largest absolute values of Laplacian eigenvalues of digraphs
No full textLet be the Laplacian matrix of a digraph and be the sum of the largest absolute values of Laplacian eigenvalues of . Let be a digraph with vertices obtained from the directed cycle by attaching a pendant arc whose tail is on . A digraph is -free if it contains no as a subdigraph for any . In this paper, we present lower bounds of of digraphs of order . We provide the exact values of of directed cycles and -free unicyclic digraphs. Moreover, we obtain upper bounds of of -free digraphs which have vertex-disjoint directed cycles
Shell extremal eigenvalues of tridiagonal Toeplitz Matrices
No full textThe shell of a complex tridiagonal Toeplitz matrix is studied. Closed formulas for all quantities involved in its equation are presented. Necessary and sufficient conditions for a Toeplitz tridiagonal matrix to have shell extremal eigenvalues are given. Several, recently introduced, geometric quantities related to the shell are studied as measures of non-normality of these extremal eigenvalues of such matrices. These quantities are also proposed as measures of non-normality for the matrix itself
