Abstract Multilinear Algebra
This presentation by Gyula Rabai introduces Abstract Multilinear Algebra by building mathematical structures from the ground up, starting with the fundamental question: what is a number? It progressively develops key algebraic concepts such as sets, magmas, monoids, groups, rings, and fields, highlighting the axioms that define each structure. From there, it connects these abstract foundations to vector spaces, showing how vectors, matrices, polynomials, and functions all fit within the same algebraic framework. Then we distill linear algebra into its essential properties before extending the discussion to multilinear algebra and tensor products. Overall, the presentation offers a concise, conceptual roadmap from basic algebraic structures to the core ideas behind multilinear algebra.
This presentation was given to:
Mathematics Society, Colchester Grammar School, 2nd July 2025
Download slide show: Abstract-Multilinear-Algebra.pptx