Multilinear algebra

shorthand notation for tensor operations

ternary operation on vectors

linear functional on tensor product square of a vector space

lines in 3D that do not intersect and neither do they point the same direction

branch of mathematics

polynomial whose nonzero terms all have the same degree

assignment of a tensor continuously varying across a mathematical space

from two vector spaces to a third one

from two vector spaces to a third one

algebraic construction used in Euclidean geometry

universal construction in multilinear algebra

thumb | right | alt=Johann Friedrich Pfaff | Johann Friedrich Pfaff In mathematics, the determinant of an m-by-m skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depends on m. When m is odd, the polynomial is zero, and when m is even, it is a nonzero polynomial of degree m/2, and is unique up to multiplication by ±1. The convention on skew-symmetric tridiagonal matrices, given below in the examples, then determines one specific polynomial, called the Pfaffian polynomial. The value of this polyn

thumb|170px|Parallel plane segments with the same orientation and area corresponding to the same bivector .

mathematical identity in algebra

thumb|Relations between scalars, vectors, simple -vectors, -vectors, and multivectors. Depending on the authors, a "multivector" may be either homogeneous or a mixture of different values of . This graph picks the latter.

algebra of all possible symmetric tensors over a vector space or ring module

method of assigning coordinates to every line in projective 3-space

theorem

binary operation between a vector field and a differential form

operation that pairs a left and a right 𝑅‐module into an abelian group

homogeneous polynomial of degree 3