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A frame is an equal norm frame if there is a constant such that ‖ ‖ = for each ... Rocky Mountain Journal of Mathematics. 51 (1). arXiv: 2004.11729.
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.
Frame homomorphisms are maps between frames that respect all joins (in particular, the least element of the lattice) and finite meets (in particular, the greatest element of the lattice). Frames, together with frame homomorphisms, form a category. The opposite category of the category of frames is known as the category of locales.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
In mathematics, a frame bundle is a principal fiber bundle associated with any vector bundle. The fiber of F ( E ) {\displaystyle F(E)} over a point x {\displaystyle x} is the set of all ordered bases , or frames , for E x {\displaystyle E_{x}} .
An ordered basis, especially when used in conjunction with an origin, is also called a coordinate frame or simply a frame (for example, a Cartesian frame or an affine frame). Let, as usual, be the set of the n-tuples of elements of F. This set is an F-vector space, with addition and scalar multiplication defined component-wise.
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.
A coordinate system in mathematics is a facet of geometry or of algebra, [9] [10] in particular, a property of manifolds (for example, in physics, configuration spaces or phase spaces). [11] [12] The coordinates of a point r in an n-dimensional space are simply an ordered set of n numbers: [13] [14]
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