Abstract. We study the generalized eigenproblem A ⊗ x = λ ⊗ B ⊗ x, where A, B ∈ R m×n in the max-plus algebra. It is known that if A and B are symmetric, then there is at most one generalized eigenvalue, but no description of this unique candidate is known in general. We prove that if C = A − B is symmetric, then the common value of all saddle points of C (if any) is the unique candidate for λ. We also explicitly describe the whole spectrum in the case when B is an outer product. It follows that when A is symmetric and B is constant, the smallest column maximum of A is the unique candidate for λ. Finally, we provide a complete description of the spectrum when n = 2.
The COVID-19 pandemic has forced us to reconsider the way we teach our students. The inability of UK-based lecturers to deliver via traditional lecture-based courses in China (due to ongoing travel restrictions) has been an obstacle to overcome but also an opportunity to investigate innovative remote-teaching methods. Here we review a case study based on teaching three different year groups at the Jinan University - University of Birmingham Joint Institute during the early part of 2020. We reflect on how technology was used, draw conclusions and discuss potential opportunities for the future of remote-teaching.
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