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Gibbs, E. (2021). Coal Country: The Meaning and Memory of Deindustrialization in Postwar Scotland. University of London Press.
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Bell, K. (2020). Working-Class Environmentalism: An Agenda for a Just and Fair Transition to Sustainability. Palgrave Macmillan
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Techniques for determining equality of the maximum nullity and the zero forcing number of a graph
No full textIt is known that the zero forcing number of a graph is an upper bound for the maximum nullity of the graph (see [AIM Minimum Rank - Special Graphs Work Group (F. Barioli, W. Barrett, S. Butler, S. Cioab, D. Cvetkovi, S. Fallat, C. Godsil, W. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I. Sciriha, W. So, D. Stevanovi, H. van der Holst, K. Vander Meulen, and A. Wangsness). Linear Algebra Appl., 428(7):1628--1648, 2008]). In this paper, we search for characteristics of a graph that guarantee the maximum nullity of the graph and the zero forcing number of the graph are the same by studying a variety of graph parameters that give lower bounds on the maximum nullity of a graph. Inparticular, we introduce a new graph parameter which acts as a lower bound for the maximum nullity of the graph. As a result, we show that the Aztec Diamond graph's maximum nullity and zero forcing number are the same. Other graph parameters that are considered are a Colin de Verdiére type parameter and vertex connectivity. We also use matrices, such as a divisor matrix of a graph and an equitable partition of the adjacency matrix of a graph, to establish a lower bound for the nullity of the graph's adjacency matrix
On the density of semisimple matrices in indefinite scalar product spaces
No full textFor an indefinite scalar product for on , it is shown that the set of diagonalizable matrices is dense in the set of all -normal matrices. The analogous statement is also proven for the sets of -selfadjoint, -skewadjoint and -unitary matrices
Corrigendum to "Determinants of Normalized Bohemian Upper Hessenberg Matrices"
No full textAn amended version of Proposition 3.6 of [Fasi and Negri Porzio, Electron. J. Linear Algebra 36:352--366, 2020] is presented. The result shows that the set of possible determinants of upper Hessenberg matrices with ones on the subdiagonal and elements in the upper triangular part drawn from the set is , instead of as previously stated. This does not affect the main results of the article being corrected and shows that Conjecture 20 in the Characteristic Polynomial Database is true
mth roots of H-selfadjoint matrices over the quaternions
No full textThe complex matrix representation for a quaternion matrix is used in this paper to find necessary and sufficient conditions for the existence of an -selfadjoint th root of a given -selfadjoint quaternion matrix. In the process, when such an -selfadjoint th root exists, its construction is also given.
 
Potentially stable and 5-by-5 spectrally arbitrary tree sign pattern matrices with all edges negative
No full textCharacterization of potentially stable sign pattern matrices has been a long-standing open problem. In this paper, we give some sufficient conditions for tree sign pattern matrices with all edges negative to allow a properly signed nest. We also characterize potentially stable star and path sign pattern matrices with all edges negative. We give a conjecture on characterizing potentially stable tree sign pattern matrices with all edges negative in terms of allowing a properly signed nest which is verified to be true for sign pattern matrices up to order 6. Finally, we characterize all 5-by-5 spectrally arbitrary tree sign pattern matrices with all edges negative
Karamardian Matrices: An Analogue of Q-Matrices
No full textA real square matrix is called a -matrix if the linear complementarity problem LCP has a solution for all . This means that for every vector there exists a vector such that , and . A well-known result of Karamardian states that if the problems LCP and LCP for some d\in \mathbb{R}^n, d >0 have only the zero solution, then is a -matrix. Upon relaxing the requirement on the vectors and so that the vector belongs to the translation of the nonnegative orthant by the null space of , belongs to its interior, and imposing the additional condition on the solution vector to be in the intersection of the range space of with the nonnegative orthant, in the two problems as above, the authors introduce a new class of matrices called Karamardian matrices, wherein these two modified problems have only zero as a solution. In this article, a systematic treatment of these matrices is undertaken. Among other things, it is shown how Karamardian matrices have properties that are analogous to those of -matrices. A subclass of a recently introduced notion of -matrices is shown to possess the Karamardian property, and for this reason we undertake a thorough study of -matrices and make some fundamental contributions