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An equal norm frame is a normalized frame (sometimes called a unit-norm frame) if =. [21] A unit-norm Parseval frame is an orthonormal basis; such a frame satisfies Parseval's identity . Equiangular frames
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
The term was coined when variables began to be used for sets and mathematical structures. onto A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e ...
In linear algebra, a k-frame is an ordered set of k linearly independent [citation needed] vectors in a vector space; thus, k ≤ n, where n is the dimension of the space, and an n-frame is precisely an ordered basis. If the vectors are orthogonal, or orthonormal, the frame is called an orthogonal frame, or orthonormal frame, respectively.
The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three Cartesian coordinates , which are the signed distances from the point to three mutually perpendicular planes.
Consider a partially ordered set (P, ≤) that is a complete lattice.Then P is a complete Heyting algebra or frame if any of the following equivalent conditions hold: . P is a Heyting algebra, i.e. the operation () has a right adjoint (also called the lower adjoint of a (monotone) Galois connection), for each element x of P.
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