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Between trilinear coordinates and distances from sidelines [ edit ] For any choice of trilinear coordinates x : y : z to locate a point, the actual distances of the point from the sidelines are given by a' = kx , b' = ky , c' = kz where k can be determined by the formula k = 2 Δ a x + b y + c z {\displaystyle k={\tfrac {2\Delta }{ax+by+cz ...
Any bilinear map is a multilinear map. For example, any inner product on a -vector space is a multilinear map, as is the cross product of vectors in .; The determinant of a matrix is an alternating multilinear function of the columns (or rows) of a square matrix.
In general, for a vector space V over a field F, a bilinear form on V is the same as a bilinear map V × V → F. If V is a vector space with dual space V ∗, then the canonical evaluation map, b(f, v) = f(v) is a bilinear map from V ∗ × V to the base field. Let V and W be vector spaces over the same base field F.
In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:
Trilinear interpolation is the extension of linear interpolation, which operates in spaces with dimension =, and bilinear interpolation, which operates with dimension =, to dimension =. These interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires 2 D = 8 {\displaystyle 2^{D}=8} adjacent pre-defined ...
Bilinear and trilinear interpolation, using multivariate polynomials with two or three variables; Zhegalkin polynomial, a multilinear polynomial over ; Multilinear form and multilinear map, multilinear functions that are strictly linear (not affine) in each variable; Linear form, a multivariate linear function
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.A bilinear form is linear in each of its arguments, but a sesquilinear form allows one of the arguments to be "twisted" in a semilinear manner, thus the name; which originates from the Latin numerical prefix sesqui-meaning "one and a ...
In abstract algebra and multilinear algebra, a multilinear form on a vector space over a field is a map: that is separately -linear in each of its arguments. [1] More generally, one can define multilinear forms on a module over a commutative ring.