section_path: Extensions and generalizations/Multilinear algebra and tensors
section_name: Multilinear algebra and tensors
paragraph_text: Multilinear algebra and tensors
  
  In multilinear algebra, one considers multivariable linear transformations, that is, mappings that are linear in each of a number of different variables. This line of inquiry naturally leads to the idea of the dual space, the vector space V* consisting of linear maps f : V → F where F is the field of scalars. Multilinear maps T : V → F can be described via tensor products of elements of V*.
  
  If, in addition to vector addition and scalar multiplication, there is a bilinear vector product V × V → V, the vector space is called an algebra; for instance, associative algebras are algebras with an associate vector product (like the algebra of square matrices, or the algebra of polynomials).