Description: Define orthogonal
complement of a subset (usually a subspace) of Hilbert
space. The orthogonal complement is the set of all vectors orthogonal
to all vectors in the subset. See ocval 26982 and chocvali 27001 for its
value. Textbooks usually denote this unary operation with the symbol
as a
small superscript, although Mittelstaedt uses the symbol as
a prefix operation. Here we define a function (prefix operation)
rather
than introducing a new syntactic form. This lets us take
advantage of the theorems about functions that we already have proved
under set theory. Definition of [Mittelstaedt] p. 9. (Contributed by
NM, 7-Aug-2000.) (New usage is discouraged.) |