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Topic: Similarity transformation

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	Generalization of Napoleon's Theorem
		The three similar triangles may be of various shapes and, in addition, one is permitted to connect any three corresponding points (and not just centroids) in order to obtain a fourth similar triangle.
		Therefore, A' is obtained from A by a spiral similarity with center N, angle ANA' and ratio NA:NA'.
		Therefore, C is obtained from A by a spiral similarity with center N, angle ANC and ratio NA:NC.
	www.cut-the-knot.org /Generalization/napoleon.shtml (883 words)

	Similarity (mathematics) - Wikipedia, the free encyclopedia
		A similarity is a composition of a homothety and an isometry.
		Suppose that triangle ABC is similar to triangle DEF in such a way that the angle at vertex A is congruent with the angle at vertex D, the angle at B is congruent with the angle at E, and the angle at C is congruent with the angle at F.
		Similarity of matrices does not depend on the base field: if L is a field containing K as a subfield, and A and B are two matrices over K, then A and B are similar as matrices over K if and only if they are similar as matrices over L.
	www.wikipedia.org /wiki/Similarity_transformation (1162 words)

	Chapter 3 (Site not responding. Last check: 2007-11-05)
		SYMMETRY IN A similarity symmetry group is any group of similarity transformations (H.S.M. Coxeter, 1969, pp.
		According to the theorem on the existence of an invariant point of every discrete similarity transformation that is not an isometry (E.I. Galyarski, A.M. Zamorzaev, 1963; H.S.M. Coxeter, 1969), all the similarity symmetry groups of the plane E
		belong to the similarity symmetry groups with an invariant point.
	www.emis.de /monographs/jablan/chap3.htm (147 words)

	Homothetic transformation - Wikipedia, the free encyclopedia
		In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin.
		The number c by which distances are multiplied is called the dilation factor or similitude ratio.
		A homothety is an affine transformation (if the fixed point is the origin: a linear transformation) and also a similarity transformation.
	en.wikipedia.org /wiki/Homothety (156 words)

	Data Quality software – Similarity Systems, ATHANOR
		Similarity Systems' AXIO 5.0 and ATHANOR 3.0 empower the relevant people in your organization to design, deploy and manage implement effective and lasting data quality processes.
		Similarity Systems is the leading provider of business-focused data quality solutions.
		Similarity Systems ATHANOR and AXIO provide businesses and government organizations with the most complete platform for successful planning and execution of data quality initiatives.
	www.evoke.com /com_about.htm (297 words)

	Similarity transformation method for data processing and visualization - US Patent 6714868 (Site not responding. Last check: 2007-11-05)
		The similarity transform method provides a framework for extracting generic function shape information, in the form of non-dimensional shape function, from data, numerical simulations, or analytic model.
		More particularly, it relates to a similarity transformation method of representing physical or computer generated data or functions on a discrete grid of one or more independent coordinates for use in a variety of computer applications.
		The transformation represented by varying "m" is generally referred to as "similarity transformation", since the transformation maintains the non-dimensional shape characteristics embedded in g
	www.patentstorm.us /patents/6714868.html (4356 words)

	GDA94 Further Transformation Options
		Similarity Transformation can be employed with either 3, 4 or 7-parameters.
		The 7-parameter transformation uses all 7 parameters and can transform coordinates between two datum's which may disagree by a shift, rotation and a scale factor.
		The accuracy of a 7-parameter transformation is reliant upon the accuracy of the parameters supplied.
	www.land.vic.gov.au /land/lcnlc2.nsf/LinkView/6FAAFDDA64BB9F4B4A256A25000A2C78E72AC6696E702F92CA256E55001BCFE3 (231 words)

	DPIWE - Transformation of Coordinates (Site not responding. Last check: 2007-11-05)
		Three methods of transforming coordinates from the Australian Geodetic Datum 1966 to the Geocentric Datum of Australia 1994 are detailed below.
		Similarity transformation parameters to convert between AGD and GDA have been developed for Tasmania, these have an estimated maximum error of 0.5m.
		This involves a similarity transformation, which is then refined further by distortion modelling.
	www.dpiwe.tas.gov.au /inter.nsf/WebPages/JGAY-53M66D?open (560 words)

	Example-based translation method and system which calculates word similarity degrees, a priori probability, and ...
		word similarity degree calculating means for calculating a word similarity degree expressing a similarity between a word of said syntax unit and a word of said example on the basis of said thesaurus and outputting said word similarity degree as said word replacement probability.
		Referring to this thesaurus, the similarity degree calculating part 54 calculates a degree of similarity between the first language sentence and the examples on the basis of the classes to which concepts common to words constituting the first language sentence and words constituting the examples belong.
		The set of word transforming operators which transform the example phrase E to match the input phrase I according to this optimum path (alignment) are the optimum word transforming operators.
	www.freepatentsonline.com /6161083.html (10624 words)

	National GPS Network information: a guide to coordinate systems in Great Britain 6
		A geodetic transformation is a mathematical operation which takes the coordinates of a point in one coordinate system and returns the coordinates of the same point in a second coordinate system.
		To properly understand geodetic transformations, it is essential to understand the relationship between a datum and the TRF that realises the datum.
		When this transformation is applied to a TRF, it has the effect of rotating and translating the network of points relative to the Cartesian axes, and applying an overall scale factor (that is, a change of size), while leaving the shape of the figure unchanged.
	www.gps.gov.uk /guide6.asp (2869 words)

	Use of Similarity Transformations to Improve GPS Heighting
		As previously mentioned the control GPS points are only located in the state of Johor, whereas the comparisons mentioned in Sections 2.1, 2.2 and 2.3 encompass the whole of the Peninsular Malaysia.
		Table 2: Statistical summary using CG2 to derive the coefficients for the similarity transformation and polynomial fitting at 25 GPS points.
		Table 3: Statistical summary using CG1 to derive the coefficients for the similarity transformation and polynomial fitting at 25 GPS points.
	www.gisdevelopment.net /technology/gps/ma03007b.htm (545 words)

	Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of ...
		Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal 1
		Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal
		In this paper we describe an orthogonal similarity transformation for transforming arbitrary symmetric matrices into a diagonal-plus-semiseparable matrix, where we can freely choose the diagonal.
	www.cs.kuleuven.ac.be /~raf/homepage/publications/papers_html/stossd (210 words)

	Recovery of the Matrix Operators in the Similarity and Congruency Transformations: Applications in Polarimetry -- from ...
		Formulas are presented for the recovery of the matrix operators in arbitrary-order similarity and congruency transformations.
		The congruency transformation is the natural form for the quantum observables of a multiple-element wave function, e.g., for polarized-light transfer: the recovery of the Jones matrix for a nondepolarizing device is demonstrated, given any three linearly independent partially polarized input Stokes states.
		It is pointed out that the geometric property is a purely mathematical property of quantum observables that arises without referring to spatial characteristics for the underlying wave function.
	library.wolfram.com /infocenter/Articles/2473 (212 words)

	Unknown (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath (Site not responding. Last check: 2007-11-05)
		Traditional polygonal approximation algorithms handle only images that are related by a similarity transformation.
		The transformation of a planar shape as the viewpoint changes with a perspective camera is a general projective one.
		In this paper, we present a novel method for polygonal approximation of closed curves that is invariant to projective transformation.
	smealsearch.psu.edu /95870.html (250 words)

	PARAMETERS, US Army War College Quarterly - Autumn 2001
		The purpose of this article is to demonstrate how those two doctrines will influence the transformation of the US Army as it struggles to move forward toward a genuine revolution in military affairs, and how that transformation process can in turn mitigate the worst excesses of both doctrines.
		The key to Army relevancy is an Army transformation process that rests on four foundations: the conduct of future war, the future operating environment, the increasing significance of full-spectrum operations, and the diminished utility of the current force.
		Given the charter of Army transformation, there is little to be gained in terms of technology, doctrine, and organization experimentation by using the Interim Force in peace operations.
	carlisle-www.army.mil /usawc/Parameters/01autumn/Jablonsk.htm (7542 words)

	Similarity Solutions of a Boundary Layer Problem over Moving Surfaces (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		Abstract: In this paper, we present the idea of nonclassical similarity transformation, which takes into account the effect of the parameter on the boundary layer thickness, where is the ratio of wall velocity to the free stream velocity.
		The transformation is applied to the fluid flow over a moving flat plate (Blasius profiles).
		Keywords---Nonclassical similarity transformation, Moving flat plate, Similarity solution.
	citeseer.ist.psu.edu /425690.html (286 words)

	State transformation in event driven explicit simulation (Site not responding. Last check: 2007-11-05)
		This paper presents a general method for incorporating state transformation in event driven explicit simulation.
		In principle, any similarity transformation of the state equation can be employed to transform the circuit into a more convenient state space for numerical solution.
		This paper develops a systematic scheme to derive an appropriate state transformation, and to incorporate the state transformulation in such a way to maintain the efficiency of event driven explicit simulation algorithms.
	doi.ieeecs.org /DOIResolver/resolver/10.1109/ICCAD.1997.643533 (220 words)

	Similar Flows and Similarity Transformation (Site not responding. Last check: 2007-11-05)
		CVO Website - Scott, et.al., Catastrophic Debris Flows Transformed from Landslid...
		Market Transformation and the adoption and diffusion of innovation Main...
		Cultural Transition and Spiritual Transformation: From Alexander the Great to Cy...
	www.scienceoxygen.com /aviation/70.html (319 words)

	Block-Triangularizations of Partitioned Matrices under Similarity/Equivalence Transformations
		This paper addresses the problem of the block-triangularization of a partitioned matrix under similarity/equivalence transformation with respect to its partitions of the column- and row-sets.
		Such block-triangularization affords a mathematical representation of the hierarchical decomposition of a physical system into subsystems if the transformation used is of physical significance.
		The results cover many block-triangularization methods hitherto discussed in the literature such as the Jordan normal form and the strongly connected-component decomposition in the case of partition-respecting similarity transformations, and the rank normal form, the Dulmage--Mendelsohn decomposition, and the combinatorial canonical form of layered mixed matrices in the case of partition-respecting equivalence transformations.
	epubs.siam.org /sam-bin/dbq/article/23559 (214 words)

	pclatrd an unitary similarity transformation Qâ * sub( A ) * Q, and returns the ma... (Site not responding. Last check: 2007-11-05)
		an unitary similarity transformation Qâ * sub(A) * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of sub(A)
		There is currently no version of the SDSM library with support for a default integer size of 8 bytes (64 bits).
		PCLATRD reduces NB rows and columns of a complex Hermitian distributed matrix sub(A) = A(IA:IA+N-1,JA:JA+N-1) to complex tridiagonal form by an unitary similarity transformation Qâ * sub(A) * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of sub(A).
	www.uni-kiel.de /rz/nvv/altix-doc/man_html/man3/pclatrd.3s.html (1001 words)

	IRIX: complib/zgehd2
		ZGEHD2 - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
		ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation: Q' * A * Q = H.
		N (input) INTEGER The order of the matrix A. ILO (input) INTEGER IHI (input) INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to ZGEBAL; otherwise they should be set to 1 and N respectively.
	nixdoc.net /man-pages/IRIX/man3/complib/zgehd2.3.html (596 words)

	DisCo - The Distributed Computing Group at Daresbury Laboratory
		This benchmark involves performing a series of similarity transforms (Q*HQ) using both a scalar and vector algorithm.
		The scalar code collapses the matrix transposition and multiplications to yield an algorithm with fewer FLOPS than the vector code, which adopts a brute force approach by explicitly performing the transposition and two matrix multiplications.
		In that benchmark, the matrices were of order 10, 20, 30,...,150, the summed CPU times referring to 150 transforms of order 10 matrices, 140 of order 20 matrices, and so on up to 10 transforms for matrices of order 150.
	www.cse.clrc.ac.uk /disco/Benchmarks/similarity.shtml (272 words)

	Similarity Transformation to Hessenberg Form (Site not responding. Last check: 2007-11-05)
		Below are two routines which reduce a square matrix to a similar upper Hessenberg matrix.
		The first routine uses a sequence of Householder transformations to reduce the input matrix to upper Hessenberg form and the second routine uses a sequence of elementary transformations to reduce the input matrix to upper Hessenberg form.
		A Householder transformation is an orthogonal transformation of the form
	mymathlib.webtrellis.net /matrices/eigen/hessenberg.html (297 words)

	Multispectal Image Similarity Transformation
		The registration software can be used to register similar or dissimilar multi-sensor imagery as long as the transformation between this imagery is restricted to rotation, translation, and scaling (collectively known as a "similarity transformation").
		Additionally, in the images ortho1_r7_s95_t20.pgm and ortho1_r7_s95.pgm the boundaries created by the transformation were filled in by hand separately in each case.
		Several lines were found in the hand-drawn areas in the non-translated image that were not present in the translated image, and these contributed to the ratio of areas enough to skew the results to a different histogram bin.
	www.lnk.com /mist/mist.html (3929 words)

	Similarity Transformation
		A similarity transformation based on the inverse of that matrix can be used to represent the system in its canonical form.
		Another way to look at this option is that it allows backward transformation from basis
		Further performance gain can be achieved if the transformation matrix is known to be orthogonal, in which case the transpose of the matrix can be used instead of its inverse.
	documents.wolfram.com /applications/control/Realizations/8.7.html (153 words)

	Structural Similarity as Guidance in Case-Based Design - Borner (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		This paper presents a novel approach to determine structural similarity as guidance for adaptation in case-based reasoning (Cbr).
		We advance structural similarity assessment which provides not only a single numeric value but the most specific structure two cases have in common, inclusive of the modification rules needed to obtain this structure from the two cases.
		Structural Similarity and Adaptation - Börner, Pippig, Tammer, Coulon (1996)
	citeseer.lcs.mit.edu /borner93structural.html (447 words)

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