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An observational frame of reference, often referred to as a physical frame of reference, a frame of reference, or simply a frame, is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized only by its state of motion. [19]
It is one of several widely used low-dimensional embedding methods. [1] Isomap is used for computing a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points. The algorithm provides a simple method for estimating the intrinsic geometry of a data manifold based on a rough estimate of each data point’s neighbors on ...
A projective frame on n-dimensional projective space is an ordered collection of n+2 points such that any subset of n+1 points is linearly independent. Frame fields in general relativity are four-dimensional frames, or vierbeins, in German. In each of these examples, the collection of all frames is homogeneous in a certain sense.
In physics, a frame of reference is often a useful way of defining a particular state of motion, the expected properties of a set of objects with a common state of motion, or how physics may appear to an observer with a state of motion. It is usually used to define a coordinate system that can be used as a reference for measurements and ...
An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g. x′, y′, a′. The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R .
A projective frame is sometimes called a simplex, [1] although a simplex in a space of dimension n has at most n + 1 vertices. In this article, only projective spaces over a field K are considered, although most results can be generalized to projective spaces over a division ring. Let P(V) be a projective space of dimension n, where V is a K ...
A projective frame is sometimes called a simplex, [6] although a simplex in a space of dimension n has at most n + 1 vertices. Projective spaces over a commutative field K are considered in this section, although most results may be generalized to projective spaces over a division ring. Let P(V) be a projective space of dimension n, where V is ...
The set of coordinates that define the position of a reference point and the orientation of a coordinate frame attached to a rigid body in three-dimensional space form its configuration space, often denoted () where represents the coordinates of the origin of the frame attached to the body, and () represents the rotation matrices that define the orientation of this frame relative to a ground ...