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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
Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require ...
The observer in this frame uses the coordinates (x, y, z, t) to describe a spacetime event, shown as a star. Although the term "coordinate system" is often used (particularly by physicists) in a nontechnical sense, the term "coordinate system" does have a precise meaning in mathematics, and sometimes that is what the physicist means as well.
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.
The Frenet–Serret frame on a curve is the simplest example of a moving frame. In mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry of smooth manifolds embedded in a homogeneous space.
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.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.