A multilinear form on a vector space over a field is a map
(1)
|
such that
(2)
|
and
(3)
|
for every and any indexes .
For example, the determinant of a square matrix of degree is an -linear form for the columns or rows of a matrix.
A multilinear form on a vector space over a field is a map
(1)
|
such that
(2)
|
and
(3)
|
for every and any indexes .
For example, the determinant of a square matrix of degree is an -linear form for the columns or rows of a matrix.
This entry contributed by Marek Pomp
Pomp, Marek. "Multilinear Form." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MultilinearForm.html