Tensor Algebra and Multilinear Maps

Tensor Algebra and Multilinear Maps. Tensor products, symmetric and exterior algebras, and tensor contractions. This page collects canonical references that organise the subject and provide entry points to its main techniques.

Foundations and canonical references

The standard treatments of tensor algebra and multilinear maps approach the subject from complementary angles. Hackbusch, Tensor Spaces and Numerical Tensor Calculus (2012) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Lang, Algebra (2002) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.

Open methodological questions for tensor algebra and multilinear maps include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.