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This paper is a study of linear spaces of matrices and linear maps on matrix algebras that arise from spin systems, or spin unitaries, which are finite sets S of selfadjoint unitary matrices such that any two unitaries in S anticommute. We are especially interested in linear isomorphisms between these linear spaces of matrices such that the matricial order within these spaces is preserved; such isomorphisms are called complete order isomorphisms, which might be viewed as weaker notion of unitary similarity. The main result of this paper shows that all m-tuples of anticommuting selfadjoint unitary matrices are equivalent in this sense, meaning that there exists a unital complete order isomorphism between the unital linear subspaces that these tuples generate. We also show that the C *envelope of any operator system generated by a spin system of cardinality 2k or 2k + 1 is the simple matrix algebra M 2 k (C). As an application of the main result, we show that the free spectrahedra determined by spin unitaries depend only upon the number of the unitaries, not upon the particular choice unitaries, and we give a new, direct proof of the fact [11] that the spin ball B spin m and max ball B max m coincide as matrix convex sets in the cases m = 1, 2.

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Decolonization and Indigenous education are at the forefront of Canadian content currently in Academia. Over the last few decades, we have seen some major changes in the way in which we share information. In particular, we have moved into an age of electronically-shared content, and there is an increasing expectation in Canada that this content is both culturally significant and relevant. In this paper, we discuss an ongoing community engagement initiative with First Nations communities in the Western Manitoba region. The initiative involves knowledge-sharing activities that focus on the topic of cybersecurity, and are aimed at a public audience. This initial look into our educational project focuses on the conceptual analysis and planning stage. We are developing a "Cybersecurity 101" mini-curriculum, to be implemented over several one-hour long workshops aimed at diverse groups (these public workshops may include a wide range of participants, from tech-adverse to tech-savvy). Learning assessment tools have been built in to the workshop program. We have created informational and promotional pamphlets, posters, lesson plans, and feedback questionnaires which we believe instill relevance and personal connection to this topic, helping to bridge gaps in accessibility for Indigenous communities while striving to build positive, reciprocal relationships. Our methodology is to approach the subject from a community needs and priorities perspective. Activities are therefore being tailored to fit each community. We hope this will lead to increased awareness and engagement by community members. Two Indigenous student research assistants were hired to assist in this project, which has developed into a blend of community outreach on the topic of security and data protection (most notably with respect to social media and online banking) and a computing education student-led educational research project.