mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W {\displaystyle W} of a vector space V {\displaystyle...

range (which is a complement of the kernel). When these basis vectors are orthogonal to the kernel, then the projection is an orthogonal projection. When...

largest subspace of V {\displaystyle V} that is orthogonal to a given subspace is its orthogonal complement. Given a module M {\displaystyle M} and its dual...

characterized in terms of the orthogonal complement: if V is a subspace of H, then the closure of V is equal to V⊥⊥. The orthogonal complement is thus a Galois connection...

subspaces Orthogonal complement Schur complement Complement (complexity), relating to decision problems and complexity classes Complement operator (regular...

every vector to an orthogonal vector but is not identically 0 {\displaystyle 0} . Orthogonal complement The orthogonal complement of a subset C ⊆ V {\displaystyle...

vector spaces, for example, orthogonal complements exist. However, these spaces may have null vectors that are orthogonal to themselves, and consequently...

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity. Orthogonality is also used with various meanings that...

the orthogonal complement operation, provides an example of an orthocomplemented lattice that is not, in general, distributive. Some complemented lattices...

ker ⁡ ( L ) {\displaystyle V/\ker(L)} can be identified with the orthogonal complement in V of ker ⁡ ( L ) {\displaystyle \ker(L)} This is the generalization...