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Topic: Linear maps

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	[No title] (Site not responding. Last check: 2007-11-06)
		In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that respects the arithmetical operations addition and scalar multiplication defined on vector spaces, or, in other words, it "preserves linear combinations".
		For instance, the integral yields a linear map from the space of all real-valued integrable functions on some interval to R, while differentiation is a linear transformation from the space of all differentiable functions to the space of all functions.
		In the finite dimensional case and if bases have been chosen, then the composition of linear maps corresponds to the multiplication of matrices, the addition of linear maps corresponds ot the addition of matrices, and the multiplication of linear maps with scalars corresponds to the multiplication of matrices with scalars.
	www.informationgenius.com /encyclopedia/l/li/linear_transformation.html (640 words)

	Linear transformation - Wikipedia, the free encyclopedia
		In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.
		Differentiation is a linear transformation from the space of all differentiable functions to the space of all functions.
		In the finite dimensional case and if bases have been chosen, then the composition of linear maps corresponds to the multiplication of matrices, the addition of linear maps corresponds to the addition of matrices, and the multiplication of linear maps with scalars corresponds to the multiplication of matrices with scalars.
	en.wikipedia.org /wiki/Linear_transformation (1103 words)

	Learn more about Linear algebra in the online encyclopedia. (Site not responding. Last check: 2007-11-06)
		Linear algebra is the branch of mathematics concerned with the study of vectorss, vector spaces (or linear spaces), linear transformations, and systems of linear equations.
		Linear algebra today has been extended to consider n-space, since most of the useful results from 2 and 3-space can be extended to n-dimensional space, but we may also use linear algebra to investigate infinite-dimensional spaces.
		Some striking examples of this are the group of invertible linear maps or matrices, and the ring of linear maps of a vector space.
	www.onlineencyclopedia.org /l/li/linear_algebra_1.html (809 words)

	Linear algebra Article, Linearalgebra Information (Site not responding. Last check: 2007-11-06)
		Linear algebra is the branch of mathematics concernedwith the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations.
		Linear operators take elementsfrom a linear space to another (or to itself), in a manner that is compatible with the addition and scalar multiplication givenon the vector space(s).
		The general method of finding a linear way to look at a problem, expressing this in terms of linear algebra, and solving it,if need be by matrix calculations, is one of the most generally applicable in mathematics.
	www.anoca.org /space/vector/linear_algebra.html (792 words)

	math129b
		To familiarize students with the language of vector spaces and linear maps, and to lead students to a deeper understanding of the structure of linear maps on vector spaces.
		Linear Algebra is the study of linear maps on finite dimensional vector spaces.
		Linear Algebra II (Math129B) emphases abstract vector spaces and linear maps.
	www.sjsu.edu /faculty/wso/math129b.htm (97 words)

	PlanetMath: linear transformation
		linear map, vector space homomorphism, linear mapping, linear operator
		linear transformation is continuous if its domain is finite dimensional
		This is version 11 of linear transformation, born on 2001-11-07, modified 2004-09-24.
	planetmath.org /encyclopedia/LinearTransformation.html (180 words)

	Linear algebra (Site not responding. Last check: 2007-11-06)
		Linear operators take elements from a linear space to another (or to itself), in a manner that is compatible with the addition and scalar multiplication given on the vector space(s).
		If a basis for a vector space is fixed, every linear transform can be represented by a table of numbers called a matrix.
		A matrix is non-singular iff the linear transformation represented by the matrix is isomorphism.
	www.sciencedaily.com /encyclopedia/linear_algebra_1 (848 words)

	Help -- Linear Maps (Site not responding. Last check: 2007-11-06)
		The marker order shown in the linear maps is identical to the 2D-map marker order, i.e., map order was determined using 2RR (the two-recombinant rule) and the transitive properties of ordered markers; markers were NOT ordered using likelihood methods used by multipoint linkage programs such as CRI-MAP.
		Map orientation: the p-terminal end of the chromosome is at the top, running down through the centromere region, and continues to the q-terminal regions.
		The segments are scaled to correspond to marker positions on the linear map (the heavy line with tie-lines to marker names).
	www.genlink.wustl.edu /mmp/help_linear_map.html (256 words)

	New York State Library: Annotated Bibliography of Selected New York State Maps: 1793-1900 (Site not responding. Last check: 2007-11-06)
		Map production responded to pressing needs, particularly transportation information: canal maps in the 1820's and 1830's, railroad maps and travellers' guides from the 1830's to the turn of the century, large scale county maps in the mid 1800s, cyclists' and thematic (economic and geological) maps by the 1890's.
		Maps were reversed on a soft copper plate and the original engraved to produce a backwards-reading intaglio template.
		Maps have particular problems in terms of "authorship" and "copyright", for a map may be copied with minor changes and become the "property" of a new author, or the publisher may buy the copyright from the author.
	www.nysl.nysed.gov /msscfa/mapsbibl.htm (10868 words)

	Linear Maps (Site not responding. Last check: 2007-11-06)
		In particular we will focus on linear maps, and we will see that linear maps may be used to solve many types of problems in mathematics including dynamical systems and Markov processes.
		In particular we will discover that every linear map between vector spaces may be represented by a matrix.
		This is the fourth abstraction, and it will allow us to analyse linear maps by their matrix representation.
	isolatium.uhh.hawaii.edu /linear/Maps.htm (115 words)

	► » Re: Linear algebra _ linear maps (Site not responding. Last check: 2007-11-06)
		► » Re: Linear algebra _ linear maps
		subspace of V can be extended to a linear map on V. Let V be a finite dimensional vector space, U be a subspace of V and T a
		linear map on U. I know that we have : if u'1' and u'2' are vectors of U and if b is a
	www.science-chat.org /Re-Linear-algebra--linear-maps-6924108.html (147 words)

	RR Kit - Maps (Site not responding. Last check: 2007-11-06)
		Extract the map packs (.zip files) into the the "SavedLevels" folder, located in the User folder in your W:A or WWP directory.
		If you have any maps you'd like to submit, you can do so here.
		Generally basic linear maps, with some interesting use of color.
	www.rrkit.com /maps.php (123 words)

	WelchWeb: Subject Guides - Basic Science (Site not responding. Last check: 2007-11-06)
		MAPS is an automated program for comparisons of multiple protein structures.
		From several homologous proteins with common structural similarities, the program can automatically superimpose the 3d models, detect which residues are structural equivalent among all the structures and provide the residue-to-residue alignment.The structurally equivalent residues are defined according to the approximate position of both main-chain and side-chain atoms of all the proteins.
		Maps of the human genome, including cytogenetic maps, linkage maps, radiation hybrid maps, content contig maps, and integrated maps.
	www.welch.jhu.edu /internet/bsci.html (3957 words)

	Linear Maps Preserving Permutation and Stochastic Matrices (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Linear Maps Preserving Permutation and Stochastic Matrices (ResearchIndex)
		We characterize those linear maps T on the linear span of S that satisfy T (S) = S. Partial results concerning those linear maps T satisfying T (S) ` S are also presented.
		1 Linear transformations on matrices: The invariance of genera..
	citeseer.ist.psu.edu /383748.html (329 words)

	The Linear Topic Map Notation
		The XML-based topic map interchange format is defined in such a way as to make it easy to understand for humans and to develop software for, and these purposes it fulfills very well.
		Humans were not really intended to do this, of course, they were intended to use specialized topic map editors, which would insulate their users from the syntactical details of the interchange format.
		This directive causes the topic map at the given URI to be loaded according to the rules of the syntax it is written in and merged with the current topic map once the loading is complete.
	www.ontopia.net /download/ltm.html (3704 words)

	Linear maps: formulae explained (Site not responding. Last check: 2007-11-06)
		We are given a formula F(X) supposed to define a linear map in 2 dimensions, say.
		Suppose that the formula has been shown to describe some linear map, but we want to show that it describes a specific linear map f (such as perpendicular projection onto a line OP).
		This is because F and f are both linear, and P and Q are a basis.
	www.maths.tcd.ie /~odunlain/1ba1/linmaps (219 words)

	I Simp6sio Brasileiro de Computaca~o e Muslca 45 (Site not responding. Last check: 2007-11-06)
		the numerical behaviour of the map in the phase-space mirrors the sonic behaviour of a waveform.
		The sequence {Xk} produced by the maps is mapped into the interval [-1,-1] to be used as waveform.
		The application of non-linear maps as sonic constructs confronts the musician with a compositional challenge: to organize chaotic sounds in a meaningful and coherent musical structure.
	www.unicamp.br /nics/publica/fragcom.htm (2475 words)

	Iterations of linear maps over finite fields - abstract (Site not responding. Last check: 2007-11-06)
		We show that the cyclic dynamics of both maps in dimension 2n can be deduced from their periodic behavior in dimension n.
		This link is generalized to a larger class of maps.
		With restrictions shared by both maps, we obtain a formula for the number of vectors in dimension 2n belonging to a cycle of length q that expresses this number in terms of the analogous values in dimension n.
	www.math.iupui.edu /~mmisiure/ducci.html (168 words)

	TkMap - a program for drawing linear maps and confidence intervals (Site not responding. Last check: 2007-11-06)
		TkMap is a bioTk program for drawing publication quality linear maps of a set of genetic or RH markers.
		TkMap is copyrighted material, but may be freely distributed under the terms of the GNU General Public License.
		I also required this patch to bioTk v1.3 map.tcl file in order to be able to correctly draw labels to the left of the map axis.
	www.hpcf.upr.edu /~humberto/software/TkMap (162 words)

	Amazon.ca: Books: Information Graphics: A Comprehensive Illustrated Reference (Site not responding. Last check: 2007-11-06)
		Covers the full spectrum of charts, graphs, maps, diagrams, and tables ranging from the most basic to the very specialized.
		While I have honed my writing skills through both experience and training in Information Mapping, I used to be at a loss about how to best portray technical data in my documents.
		This book is an overwhelming reference to all types of graphs, maps, tables, diagrams, and charts.
	www.amazon.ca /exec/obidos/ASIN/0195135326 (817 words)

	State Maps for Linear Systems
		State Maps for Linear Systems: SIAM Journal on Control and Optimization Vol.
		As such, state-space models are not a natural starting point for modeling, while they have utmost importance in the simulation and control phase.
		The paper addresses the problem of computing state variables for systems of linear differential-algebraic equations of various forms.
	epubs.siam.org /sam-bin/dbq/article/26841 (134 words)

	Howard's multichain policy iteration algorithm for max-plus linear maps (Site not responding. Last check: 2007-11-06)
		I wrote a small c-program which implements Howard's mulichain policy iteration algorithm for max-plus linear maps.
		Howard's algorithm runs in an almost linear time (although no proof of this fact exists).
		It is much faster than the classical algorithms to compute the cycle time, including Karp's.
	amadeus.inria.fr /gaubert/HOWARD.html (233 words)

	linearmaps
		"linear measure" "linear unit" linuron "lion marmoset" "lunar module" "lunar month" "Lunaria annua"
		"linear measure" "linear momentum" "loom harnessing" "low in harmful substances" "lunar module"
		"linear amplifier" "linear inheritance" "linear measures" "lunar month"
	dictionary-x.com /linearmaps.html (150 words)

	Human Chromosome 11 Linear Maps (Site not responding. Last check: 2007-11-06)
		This map displays chromosome 11 meiotic markers in the 2D map order and is based upon the same genotype data used for the 2D map.
		Markers mapping to identical positions are displayed horizontally to the right of the map location; these loci have no detectable inter-marker recombination.
		Click on segment number to view the corresponding 2D-Map.
	www.genlink.wustl.edu /mmp/chr11/linear_maps.html (56 words)

	A Nonlinear Bayesian Filter for Chaotic Piecewise Linear Maps (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		A Nonlinear Bayesian Filter for Chaotic Piecewise Linear Maps
		Abstract: In this paper we derive the Bayesian filter for chaotic signals generated by piecewise linear maps.
		We give the basic signal model containing an additive Gaussian noise and solve the Bayesian state estimation problem for the chaotic system.
	citeseer.ist.psu.edu /196357.html (235 words)

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