# Multilinear

### Some articles on multilinear:

Leibniz Formula For Determinants - Formal Statement and Proof
... exactly one function which is alternate multilinear w.r.t ... As is multilinear, one has From alternation it follows that any term with repeated indices is zero ... Therefore no function besides the function defined by the Leibniz Formula is a multilinear alternating function with ...
Pullback (differential Geometry) - Pullback of Multilinear Forms
... is an element of L(V,W), also denoted Hom(V,W)), and let be a multilinear form on W (also known as a tensor — not to be confused with a tensor field — of rank (0,s ... Then the pullback Φ*F of F by Φ is a multilinear form on V defined by precomposing F with Φ ... given vectors v1,v2...vs in V, Φ*F is defined by the formula which is a multilinear form on V ...
Multilinear Form
... In multilinear algebra, a multilinear form is a map of the type where V is a vector space over the field K, that is separately linear in each its n variables ... An important type of multilinear forms are alternating multilinear forms which have the additional property of changing their sign under exchange of two arguments ...
Multilinear Polynomial
... In algebra, a multilinear polynomial is a polynomial that is linear in each of its variables ... They are important in the study of polynomial identity testing, because if a multilinear polynomial is zero on a set of vectors that span the space, it will be zero everywhere ... The degree of a multilinear polynomial is the maximum number of distinct variables occurring in any monomial ...
Penrose Graphical Notation - Interpretations - Multilinear Algebra
... In the language of multilinear algebra, each shape represents a multilinear function ... The lines attached to shapes represent the inputs or outputs of a function, and attaching shapes together in some way is essentially the composition of functions ...