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Tensors: Old and New Motivations from Linear Algebra
John Sheekey
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Tensors are fundamental mathematical objects that arise in a variety of areas of mathematics and physics. In finite dimensions they can be seen as a natural extension of matrices to higher dimensional arrays, or more generally as multilinear maps and forms. Students often first encounter tensors in courses on differential geometry or applied mathematics. However, there are many interesting and accessible applications of tensors in the realm of linear algebra.
In this talk we will share some ideas for motivating the study of tensors in an advanced linear algebra course. We will discuss classical applications such as the complexity of multiplication in an algebra, as well as more recent applications arising from quantum information theory and post-quantum cryptography.
