In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity. Orthogonality is also used with various meanings that...
15 KB (2,571 words) - 02:40, 10 April 2024
not true; having a determinant of ±1 is no guarantee of orthogonality, even with orthogonal columns, as shown by the following counterexample. [ 2 0...
36 KB (4,802 words) - 16:45, 22 May 2024
orthogonality in the usual way, namely that two polynomials are orthogonal if their inner product is zero. Then the sequence (Pn)∞ n=0 of orthogonal polynomials...
14 KB (2,027 words) - 00:21, 18 May 2024
the orthogonality principle is a necessary and sufficient condition for the optimality of a Bayesian estimator. Loosely stated, the orthogonality principle...
9 KB (1,707 words) - 22:35, 27 May 2022
the unit disk and have orthogonality of both radial and angular parts. Walsh functions and Haar wavelets are examples of orthogonal functions with discrete...
6 KB (771 words) - 22:44, 1 January 2024
most-frequently used regarding assembly instruction sets, as orthogonal instruction set. Orthogonality in a programming language means that a relatively small...
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number λn. The interval of orthogonality is bounded by whatever roots Q has. The root of L is inside the interval of orthogonality. Letting R ( x ) = e ∫...
35 KB (6,102 words) - 20:33, 17 November 2022
form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , where orthogonality of two vectors v {\displaystyle v} and w {\displaystyle w} means ⟨ v...
3 KB (529 words) - 08:09, 13 March 2024
\langle f,g\rangle _{w}=0.} Orthogonality of two functions with respect to one inner product does not imply orthogonality with respect to another inner...
13 KB (2,164 words) - 00:04, 7 May 2024
1/m and the slopes of hyperbolic orthogonal lines are reciprocals of each other. The relation of hyperbolic orthogonality actually applies to classes of...
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In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension...
56 KB (7,820 words) - 07:00, 11 March 2024
wavelet mask. A necessary condition for the orthogonality of the wavelets is that the scaling sequence is orthogonal to any shifts of it by an even number of...
4 KB (729 words) - 19:03, 20 October 2022
In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a "table" (array) whose entries come from a fixed finite set...
27 KB (3,395 words) - 18:39, 6 October 2023
circle orthogonal to the circle of ideal points bounding the disk. Orthogonality Radical axis Power center (geometry) Apollonian circles Bipolar coordinates...
3 KB (244 words) - 23:02, 12 May 2024
In linear algebra, an orthogonal transformation is a linear transformation T : V → V on a real inner product space V, that preserves the inner product...
4 KB (723 words) - 04:23, 22 February 2024
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. This method is...
6 KB (696 words) - 03:13, 10 December 2023
In mathematics, the Schur orthogonality relations, which were proven by Issai Schur through Schur's lemma, express a central fact about representations...
14 KB (2,618 words) - 13:00, 23 May 2024
Orthogonal is a science fiction trilogy by Australian author Greg Egan taking place in a universe where, rather than three dimensions of space and one...
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the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W {\displaystyle W} of a vector space V {\displaystyle...
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Projection (linear algebra) (redirect from Orthogonal projection)
the concept of orthogonality can be used. A projection P {\displaystyle P} on a Hilbert space V {\displaystyle V} is called an orthogonal projection if...
34 KB (5,802 words) - 21:53, 28 April 2024
in 1971 with the introduction of a guard interval, providing better orthogonality in transmission channels affected by multipath propagation. Each subcarrier...
87 KB (11,280 words) - 16:55, 25 April 2024
The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational...
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In mathematics, orthogonal coordinates are defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots...
30 KB (3,359 words) - 05:27, 18 May 2024
significantly reversed the trend against more orthogonality. Modern CPUs often simulate orthogonality in a preprocessing step before performing the actual...
21 KB (3,008 words) - 12:03, 8 November 2023
Inner product space (redirect from Orthogonal vector)
definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean...
56 KB (7,305 words) - 21:43, 1 April 2024
mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure...
2 KB (278 words) - 21:45, 9 April 2024
the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are...
3 KB (343 words) - 18:10, 29 February 2024
mathematics, an orthogonal trajectory is a curve which intersects any curve of a given pencil of (planar) curves orthogonally. For example, the orthogonal trajectories...
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linear algebra, an orthogonal diagonalization of a normal matrix (e.g. a symmetric matrix) is a diagonalization by means of an orthogonal change of coordinates...
2 KB (253 words) - 07:22, 23 May 2024
Orthonormal basis (redirect from Orthogonal set)
whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space R...
14 KB (2,582 words) - 15:17, 7 May 2024