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  2. Bilinear form - Wikipedia

    en.wikipedia.org/wiki/Bilinear_form

    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:

  3. Trilinear interpolation - Wikipedia

    en.wikipedia.org/wiki/Trilinear_interpolation

    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 ...

  4. Bilinear map - Wikipedia

    en.wikipedia.org/wiki/Bilinear_map

    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.

  5. Multilinear map - Wikipedia

    en.wikipedia.org/wiki/Multilinear_map

    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.

  6. Bilinear interpolation - Wikipedia

    en.wikipedia.org/wiki/Bilinear_interpolation

    Example of bilinear interpolation on the unit square with the z values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation.

  7. Trilinear coordinates - Wikipedia

    en.wikipedia.org/wiki/Trilinear_coordinates

    In geometry, the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates .

  8. Sesquilinear form - Wikipedia

    en.wikipedia.org/wiki/Sesquilinear_form

    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 ...

  9. Trilinear - Wikipedia

    en.wikipedia.org/wiki/Trilinear

    Trilinear may refer to: Trilinear filtering, a method in computer graphics for choosing the color of a texture; Trilinear form, a type of mathematical function from a vector space to the underlying field; Trilinear interpolation, an extension of linear interpolation for interpolating functions of three variables on a rectilinear 3D grid