Multilinear Form
A multilinear form on a vector space V(F) over a field F is a map
| f:V(F)×...×V(F)->F |
(1)
|
such that
| c·f(u_1,...,u_i,...,u_n)=f(u_1,...,c·u_i,...,u_n) |
(2)
|
and
for every c in F and any indexes i,j.
For example, the determinant of a square matrix of degree n is an n-linear form for the columns or rows of a matrix.
See also
Bilinear Form, Vector SpaceThis entry contributed by Marek Pomp
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Pomp, Marek. "Multilinear Form." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MultilinearForm.html