Search results
Results from the WOW.Com Content Network
The red figure is the Minkowski sum of blue and green figures. In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B:
For a finite-dimensional inner product space of dimension , the orthogonal complement of a -dimensional subspace is an ()-dimensional subspace, and the double orthogonal complement is the original subspace: =.
In the branch of mathematics called functional analysis, a complemented subspace of a topological vector space, is a vector subspace for which there exists some other vector subspace of , called its (topological) complement in , such that is the direct sum in the category of topological vector spaces.
In a three-dimensional Euclidean vector space, the orthogonal complement of a line through the origin is the plane through the origin perpendicular to it, and vice versa. [ 5 ] Note that the geometric concept of two planes being perpendicular does not correspond to the orthogonal complement, since in three dimensions a pair of vectors, one from ...
The nines' complement of a decimal digit is the number that must be added to it to produce 9; the nines' complement of 3 is 6, the nines' complement of 7 is 2, and so on, see table. To form the nines' complement of a larger number, each digit is replaced by its nines' complement.
This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.
The proof of the connectedness of the Mandelbrot set in fact gives a formula for the uniformizing map of the complement of (and the derivative of this map). By the Koebe quarter theorem , one can then estimate the distance between the midpoint of our pixel and the Mandelbrot set up to a factor of 4.
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".