Multilinear algebra refers to the branch of mathematics that deals with multilinear mappings and tensors, also known as rank k contravariant tensors. Some synonyms for multilinear algebra include tensor calculus, tensor analysis, and multilinear algebraic geometry. Tensor calculus involves using tensors to analyze and describe curved spaces, while tensor analysis is the study of tensors and their properties. Multilinear algebraic geometry combines multilinear algebra with algebraic geometry to study the properties of multi-dimensional spaces. Other related fields include linear algebra, which deals with linear mappings and matrices, and differential geometry, which deals with smooth manifolds and their properties.