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| 1 | Orthogonal function |
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| 2 | Orthogonal functions |
| In mathematics, two functions f and g are orthogonal if their inner product is zero. Whether or not two particular functions are orthogonal depends on how their inner product has been defined. A... conditions can often be written as a weighted sum of orthogonal solution functions (a.k.a. ... | |
| 3 | Orthogonal polynomials |
| orthogonal polynomials with respect to a "weight function" w when In other words, if polynomials are... the orthogonal polynomials are simply orthogonal vectors in this inner product space. By convention... orthogonal). For example: The Hermite polynomials are orthogonal with respect to a normal probability ... | |
| 4 | Orthogonality |
| In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that... at a right angle are orthogonal to each other. Two vectors in an inner product space are orthogonal... example, in a 2- or 3-dimensional Euclidean space, two vectors are orthogonal if their dot product is ... | |
| 5 | Orthogonalization |
| In linear algebra, orthogonalization means the following: we start with vectors v 1,..., vk in an... to find mutually orthogonal vectors u 1,..., uk which generate the same subspace as the vectors v 1,..., vk . One method for performing orthogonalization is the Gram-Schmidt process. When performing ... | |
| 6 | Orthogonal projection |
| In geometry, an orthogonal projection of a k -dimensional object onto a d -dimensional hyperplane... points of an object orthogonally to the d -hyperplane. In particular, an orthogonal projection of a... the object orthogonally to the plane of projection. If such a projection leaves the origin fixed ... | |
| 7 | Orthogonal matrix |
| In linear algebra, an orthogonal matrix is a square matrix G whose transpose is its inverse, i.e.... the rest of this article. A real square matrix is orthogonal if and only if its columns form an... rows form an orthonormal basis of R n. Geometrically, orthogonal matrices describe linear ... | |
| 8 | Gábor Szegö |
| Gábor Szegö (January 20, 1895 - August 7, 1985) was a Hungarian mathematician. Szegö was born in Kunhegyes, Hungary. His most important work centered around Toeplitz matrices and orthogonal polynomials. He was a teacher of János von Neumann. His book Orthogonal polynomials published in 1939 is ... | |
| 9 | Gram-Schmidt process |
| orthogonalizing a set of vectors in an inner product space, most commonly the Euclidean space R n. Orthogonalization in this context means the following: we start with vectors v 1,..., vk which are linearly independent and we want to find mutually orthogonal vectors u 1,..., uk which generate the ... | |
| 10 | Generalized orthogonal group |
| In mathematics, the generalized orthogonal group , O( p, q ) is the Lie group of all linear... generalized special orthogonal group , SO( p, q ) is the subgroup of O( p, q ) having determinant 1. The... O( p, q ; C ) are isomorphic with the usual orthogonal group O( p + q ; C ). See also : orthogonal ... | |
| 11 | Empirical orthogonal functions |
| In statistics and signal processing, the method of empirical orthogonal functions is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The i th basis function is chosen to be orthogonal to the basis functions from the first through i ... | |
| 12 | Projection (linear algebra) |
| ‰¤ m ). A special class of projections is the class of orthogonal projections, which are self-adjoint projections. Projections (orthogonal and otherwise) play a major role in algorithms for certain ... | |
| 13 | Spinor group |
| In mathematics the spinor group Spin( n) is a particular double cover of the special orthogonal group SO( n, R ). That is, there exists a short exact sequence of Lie groups For n > 2, Spin( n) is...) therefore shares its dimension n (n - 1) / 2 and its Lie algebra with the special orthogonal group ... | |
| 14 | Component-based paradigm |
| scheme. Related articles mechatronics automata automation robot orthogonality atomicity ... | |
| 15 | Basis function |
| or orthogonal to each other, which is fulfilled by (1,0) and (0,1). In functions, we have function f... "orthogonal" to each other, but in a different way from vectors. Two vectors are orthogonal if their scalar product is zero, which means they are at right angles. Two functions are orthogonal if their ... |