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A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis.
A tennis match is composed of points, games, and sets. A set consists of a number of games (a minimum of six), which in turn each consist of points. A set is won by the first side to win six games, with a margin of at least two games over the other side (e.g. 6–4 or 7–5).
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Note that closed and bounded sets are not in general weakly compact in Hilbert spaces (consider the set consisting of an orthonormal basis in an infinite-dimensional Hilbert space which is closed and bounded but not weakly compact since it doesn't contain 0). However, bounded and weakly closed sets are weakly compact so as a consequence every ...
orthonormal 1. A subset S of a Hilbert space is orthonormal if, for each u, v in the set, , = 0 when and = when =. 2. An orthonormal basis is a maximal orthonormal set (note: it is *not* necessarily a vector space basis.) orthogonal 1.
A set of mutually orthonormal vectors in a Hilbert space is called an orthonormal system. An orthonormal basis is an orthonormal system with the additional property that the linear span of S {\displaystyle S} is dense in H {\displaystyle H} . [ 6 ]
Walsh functions and trigonometric functions are both systems that form a complete, orthonormal set of functions, an orthonormal basis in the Hilbert space [,] of the square-integrable functions on the unit interval.
In other words, the set of all orthonormal frames is a right ()-torsor. The orthonormal frame bundle of , denoted (), is the set of all orthonormal frames at each point in the base space . It can be constructed by a method entirely analogous to that of the ordinary frame bundle.
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