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# Topic: Orthogonal

###### In the News (Sun 23 Jun 19)

 Orthogonality - Wikipedia, the free encyclopedia Hence orthogonality of vectors is a generalization of the concept of perpendicular. In 4D the orthogonal complement of a line is a hyperplane and vice versa, and that of a plane is a plane. The Legendre polynomials are orthogonal with respect to the uniform distribution on the interval from −1 to 1. en.wikipedia.org /wiki/Orthogonal   (1338 words)

 Orthogonal group - Wikipedia, the free encyclopedia In even dimensions in characteristic 2 the orthogonal group is a subgroup of the symplectic group, because the symmetric bilinear form of the quadratic form is also an alternating form. For the usual orthogonal group over the reals it is trivial, but it is often non-trivial over other fields, or for the orthogonal group of a quadratic form over the reals that is not positive definite. As an algebraic group, an orthogonal group is in general neither connected nor simply-connected; the latter point brings in the spin phenomena, while the former is related to the discriminant. en.wikipedia.org /wiki/Orthogonal_group   (1448 words)

 Orthogonal Persistence - TunesWiki Orthogonal persistence is quite a natural concept, because this is exactly what people need when manipulating objects, as what counts to serious people is not (just) the fun they have during a computer session, but the work they accumulate during successive sessions. But this is no particular disadvantage of orthogonal persistence as compared to other forms of explicit persistence, since all modern operating systems have just as much problem guaranteeing commitment of data in explicitly persistent databases, and require that a special procedure be called to ensure that buffers be flushed to disk during commits or shutdown. Orthogonal persistence will change nothing about the advantages and intrinsic complexities of project management; what it will do is provide enhanced reliability through simpler and better factorized implementation, with system-side marshalling and error management. tunes.org /wiki/Orthogonal_Persistence   (1356 words)

 Orthogonal matrix In three dimesions, the orthogonal matrices with determinant 1 correspond to proper rotations and those with determinant −1 to improper rotations. The set of all orthogonal matrices whose determinant is 1 is a subgroup of O(n) of index 2, the special orthogonal group SO(n). The complex analog to orthogonal matrices are the unitary matrices. www.guajara.com /wiki/en/wikipedia/o/or/orthogonal_matrix.html   (435 words)

 PlanetMath: orthogonal This is where the use of “orthogonal” in orthogonal lines, orthogonal circles, and other geometric terms come from. In the realm of linear algebra, two vectors are orthogonal when their dot product is zero, which gave rise a generalization of two vectors on some inner product space (not necessarily dot product) being orthogonal when their inner product is zero. This is version 9 of orthogonal, born on 2002-01-04, modified 2005-03-19. planetmath.org /encyclopedia/Orthogonal.html   (219 words)

 Encyclopedia :: encyclopedia : Empirical orthogonal functions   (Site not responding. Last check: 2007-10-22) 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 ith basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance. The method of empirical orthogonal functions is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies. www.hallencyclopedia.com /Empirical_orthogonal_functions   (238 words)

 Orthogonal Latin Squares There are no orthogonal latin squares of order 2 because there are only two latin squares of order 2 in the same symbols and they are not orthogonal. Orthogonal latin squares of order 5, or any odd order, on the other hand, are not so hard to find. The diagonal sums are the same as those of the rows and columns because latin square A is orthogonal to both B and C, and one diagonal of A has all entries 0 and the other diagonal has all entries a+1. www.cut-the-knot.org /arithmetic/latin3.shtml   (1319 words)

 TS-DOC: TS-723 - Orthogonal Arrays Orthogonal arrays are frequently used as plans for conducting experiments. Every orthogonal array listed in Orthogonal Arrays (Hedayat, Sloane, and Stufken, 1999) (http://www.research.att.com/~njas/doc/OA.html) can be found here along with many arrays that were not known in 1999 and many other larger arrays as well. Orthogonal array research is an active area today, and new arrays are being discovered all of the time. support.sas.com /techsup/technote/ts723.html   (1297 words)

 orthogonal - a definition from Whatis.com Pascal is sometimes considered to be an orthogonal language, while C++ is considered to be a non-orthogonal language. Orthogonal persistence is the quality of a programming system that allows a programmer to treat data similarly without regard to the length of time the data is kept in storage. Using a programming system with orthogonal data persistence allows the programmer to treat data the same way regardless of its persistence characteristic, saving programming time and making it easier to enforce referential integrity (a type of constraint applied to ensure correct data validity). searchstorage.techtarget.com /sDefinition/0,,sid5_gci283993,00.html   (348 words)

 Orthogonal | English | Dictionary & Translation by Babylon N mutually orthogonal vectors span an N-dimensional vector space, meaning that, any vector in the space can be expressed as a linear combination of the vectors. For example, in logic, the set of operators "not" and "or" is described as orthogonal, but the set "nand", "or", and "not" is not (because any one of these can be expressed in terms of the others). Orthogonal to French Orthogonal to Italian Orthogonal to Spanish Orthogonal to Dutch Orthogonal to Portuguese Orthogonal to German Orthogonal to Russian Orthogonal to Japanese Orthogonal to Chinese (T) Orthogonal to Chinese (S) Orthogonal to Turkish Orthogonal to Hebrew Orthogonal to Additional Orthogonal to Croatian Orthogonal to Serbian Orthogonal to Swedish www.babylon.com /definition/Orthogonal   (349 words)

 Orthogonal frequency-division multiplexing - Free net encyclopedia   (Site not responding. Last check: 2007-10-22) Orthogonal frequency-division multiplexing (OFDM), also sometimes called discrete multitone modulation (DMT), is a complex modulation technique for transmission based upon the idea of frequency-division multiplexing (FDM) where each frequency channel is modulated with a simpler modulation. In OFDM the frequencies and modulation of FDM are arranged to be orthogonal witheach other which almost eliminates the interference between channels. An OFDM carrier signal is the sum of a number of orthogonal sub-carriers, with baseband data on each sub-carrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phase-shift keying (PSK). www.netipedia.com /index.php/OFDM   (2382 words)

 Construction of Orthogonal Arrays and Covering Arrays Using Permutation Groups Orthogonal arrays in diagonal form, and their elements' products, powers, and orders, are derived from first column vectors which result from the searches. This is the criterion to be used to find orthogonal arrays of vectors, for all distinct i and i', and all distinct k and k'. When c=m, the orthogonal array of plus vectors can be expressed as an m-by-m array to which the plus operator is applied. home.att.net /~gsherwood/cover.htm   (5848 words)

 4.1.3 Orthogonal Components   (Site not responding. Last check: 2007-10-22) Orthogonal components are a special kind of composite states. Orthogonal components belonging to the same (orthogonal or non-orthogonal) composite state are separated by dashed lines across the round-corner box of the composite state. If a composite state has an orthogonal component as one of its children states, all its other children states must also be orthogonal components. msdl.cs.mcgill.ca /MSDL/people/tfeng/thesis/node47.html   (221 words)

 Orthogonal Polynomials and Special Function - Summer Course Classical orthogonal polynomials in one variable are the unique set of orthogonal polynomials in one variable which can be defined by a Rodrigues type formula. Polynomials orthogonal with respect to a perturbation of certain classical weight functions by the addition of mass points at the end points of the interval \$\Omega\subset\mathbb{R}\$ are considered. During the last decade there has been an intense activity in the study of the information entropies associated to the classical orthogonal polynomials, motivated by their relevance to quantum physics and their close relationship to other interesting mathematical objects, such as the \$L^p\$-norms or the logarithmic potentials of the polynomials. www.mat.uc.pt /~ajplb/opsf2.htm   (3102 words)

 Orthogonal Arrays The columns of the orthogonal array correspond to the different variables whose effects are being analyzed. While there are nowadays other applications of orthogonal arrays in statistics (for example in computer experiments and survey sampling), the principal application is in the selection of level combinations for fractional factorial experiments. Since the rows of an orthogonal array represent runs (or tests or samples) - which require money, time, and other resources - there are always practical constraints on the number of rows that can be used in an experiment. www.research.att.com /~njas/doc/OA.html   (2415 words)

 Jargon File 3.0.0 - orthogonal   (Site not responding. Last check: 2007-10-22) Used in a generalization of its mathematical meaning to describe sets of primitives or capabilities that, like a vector basis in geometry, span the entire `capability space' of the system and are in some sense non-overlapping or mutually independent. For example, in architectures such as the PDP-11 or VAX where all or nearly all registers can be used interchangeably in any role with respect to any instruction, the register set is said to be orthogonal. Or, in logic, the set of operators `not' and `or' is orthogonal, but the set `nand', `or', and `not' is not (because any one of these can be expressed in terms of the others). www.clueless.com /jargon3.0.0/orthogonal.html   (124 words)

 Orthogonal Latin Square Designs   (Site not responding. Last check: 2007-10-22) In the orthogonal version there is the additional stipulation that for each row sequence, as read from left to right, there must be a corresponding column sequence, as read from top to bottom. Thus, in the present example, row 1 (A, B, C, D) is orthogonal with column 1 (A, B, C, D); row 2 (B, C, D, A) is orthogonal with column 2 (B, C, D, A); and so on. The analysis of variance within an orthogonal Latin Square results in three F-ratios: one for the row variable, one for the column variable, and one for the third IV whose j levels are distributed orthogonally among the cells of the rows x columns matrix. departments.vassar.edu /~lowry/lsqtext.html   (518 words)

 orthogonal - Wiktionary A chord and the radius that bisects it are orthogonal. The normal vector and tangent vector at a given point are orthogonal. The content of the message should be orthogonal to the means of its delivery. en.wiktionary.org /wiki/orthogonal   (92 words)

 Coded Orthogonal Frequency Division Multiplexing (COFDM) The property of orthogonality for communication signals means that signals that are orthogonal to each other can be transmitted together and they don't interfere with each other. So having the subcarriers all orthogonal to one another (each subcarrier is orthogonal to all the other 1535 subcarriers) means that you can transmit the subcarriers in parallel and they won't interfere with each other. To show why this retains orthogonality you have to consider that the OFDM signal consists of the addition of all the subcarrier signals, which are all at different frequencies f www.digitalradiotech.co.uk /cofdm.htm   (4724 words)

 Latin-Square Geometry: Orthogonal Latin Squares as Skew Lines   (Site not responding. Last check: 2007-10-22) The six 4x4 Latin squares that have orthogonal Latin mates can be embedded in a set of thirty-five 4x4 arrays so that orthogonality in the set of arrays corresponds to skewness in the set of 35 lines of the finite projective space PG(3,2). Two arrays are orthogonal iff their 3-sets of diagrams are disjoint, i.e. This is a new way of viewing orthogonality of Latin squares, quite different from their relationship to projective planes. m759.freeservers.com /ortho.html   (2166 words)

 Orthogonal Trajectories Indeed, it is clear that whenever one line intersects one circle, the tangent line to the circle (at the point of intersection) and the line are perpendicular or orthogonal. We say the two curves are orthogonal at the point of intersection. which happens to be the slope of the tangent line to the orthogonal curve passing by the point (x,y). www.sosmath.com /diffeq/first/orthogonal/orthogonal.html   (838 words)

 Orthogonal Persistence   (Site not responding. Last check: 2007-10-22) Small, secure, real-time microkernel with orthogonal persistence: pull the plug and restart with never a problem. Orthogonal persistence's main advantages over other methods of managing long-term data are as follows:... Orthogonal versioning implements Class evolotion (Scheme evolution), it uses similar architecture as Orthogonal persistence, but it is not much... www.orthogonalpersistence.info   (305 words)

 Orthogonal Regression In ordinary linear regression, the goal is to minimize the sum of the squared vertical distances between the y data values and the corresponding y values on the fitted line. In orthogonal regression the goal is to minimize the orthogonal (perpendicular) distances from the data points to the fitted line. For an example of a NLREG program that performs orthogonal regression to a 3D plane, please click here. www.nlreg.com /orthogonal.htm   (317 words)

 Orthogonal Vectors Find all vectors that are orthogonal both to the vector orthogonality of vectors in a Hilbert space has an additional property: To apply the orthogonalization process of proposition 1.6.8, we check first the system www.cs.ut.ee /~toomas_l/linalg/lin1/node10.html   (334 words)

 Orthogonal Arrays This is an array of size N by k, with entries from 0 to s-1, with the property that in any t columns you see each of the s^t possibilities equally often. indicates a mixed-level (or asymmetrical) orthogonal array with N runs, k1 factors at s1 levels, k2 factors at s2 levels,..., and with strength 2. That there is also a table showing the parameters of all known orthogonal arrays of strength 2 and up to 100 runs (both mixed and unmixed). www.research.att.com /~njas/oadir   (1264 words)

 OFDM, VOFDM, COFDM, Orthogonal Frequency Division Multiplexing OFDM Receivers for Broadband-Transmission OFDM and the orthogonality principle, The general problem: Data transmission over multipath channels, Single carrier approach, Multi carrier approach, Orthogonal Frequency Division Multiplexing, An OFDM receiver for DVB-T, Tasks of the inner receiver and receiver structure, Channel estimation for OFDM, Performance of the complete receiver... OFDM Tutorial Frequency division multiplexing (FDM) is a technology that transmits multiple signals simultaneously over a single transmission path, such as a cable or wireless system. Orthogonal FDM's (OFDM) spread spectrum technique distributes the data over a large number of carriers that are spaced apart at precise frequencies. www.palowireless.com /ofdm/tutorials.asp   (585 words)

 orthogonal polynomial Orthogonality has the meaning of being zero of the inproducts Some orthogonal polynomials have been given special attention, and were named to their explorer: The polynomials are also solutions of differential equations with the same name (equation of Hermite, Laguerre and so on), with whom I don't want you to torture. www.2dcurves.com /polynomial/polynomialo.html   (214 words)

 Orthogonal Trajectory   (Site not responding. Last check: 2007-10-22) In mathematics, orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles.The problem is Two curves are orthogonal if each point of intersection of their tangent lines are perpendicular An orthogonal trajectory of the family is a curve which at each point is orthogonal to the curve of the family passing through this point. www.orthogonaltrajectory.info   (329 words)

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