multilinear form

A 'multilinear form' is a mathematical function that is fundamental in the study of multilinear algebra and tensor analysis.

🇺🇸 US Voice:

🇬🇧 UK Voice:

Definition

(technical, academic)A function that takes several vectors as input and is linear in each argument individually.

In multilinear algebra, a multilinear form is used to study interactions between different vector spaces.
The multilinear form simplifies when one of the vectors is fixed.

(technical, academic)A map that assigns a scalar to a set of vectors, maintaining linearity with respect to each vector.

Multilinear forms are essential in the construction of tensors.
The properties of a multilinear form change under permutations of its arguments.

Terms that have similar or relatively close meanings to "multilinear form":