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Topic: Codomain space

	Gardener of Thoughts - Fluons
		Although space S and space D are discontinuous in the place of their fluonic fractures, but space S-D is continuous.
		space (like a sphere in a 3D space), the "jump" occurs both when an object enters in the sphere and when it exits (or just when the object exits the sphere, if the object was inside the sphere when the fluon was created).
		The continuity of the space which is in front of space S is remapped with the space which is in front of space D. Thus, an observer which looks at the back of space D would see the back of space S. Here is a graphical example.
	www.gardenerofthoughts.org /ideas/fluonmatrix/flt.htm (1734 words)

	Glossary - Linear Algebra
		The column space of a matrix is the subspace of the codomain which is spanned by the columns of the matrix.
		The dimension of the column space is called the rank of the matrix, and is equal to the dimension of the column space.
		The row space of a matrix is the subspace of the domain which is spanned by the rows of the matrix.
	www.math.umbc.edu /~campbell/Math221/Glossary (1250 words)

	PlanetMath: function spaces
		Usually domain and codomain of considered functions are fixed and they are included in the notation.
		One usually consider function spaces which are closed under operations (1) and thus are vector spaces.
		This is version 30 of function spaces, born on 2004-02-10, modified 2006-02-14.
	planetmath.org /encyclopedia/FunctionSpaces.html (444 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		Vector spaces are the basic objects of study in linear algebra, and are used throughout mathematics, science, and engineering.
		Given a vector space V, a nonempty subset W of V that is closed under addition and scalar multiplication is called a subspace of V. Subspaces of V are vector spaces (over the same field) in their own right.
		Thus vector spaces over a given field are fixed up to isomorphism by a single cardinal number (called the dimension of the vector space) representing the size of the basis.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=vector_space (1588 words)

	Continuous function (topology) - Wikipedia, the free encyclopedia
		In a metric space, it is equivalent to consider the neighbourhood system of open balls centered at x and f(x) instead of all neighborhoods.
		In several contexts, the topology of a space is conveniently specified in terms of limit points.
		A continuous functions between two topological spaces stays continuous if we strengthen the topology of the domain space or weaken the topology of the codomain space.
	en.wikipedia.org /wiki/Continuous_function_(topology) (1258 words)

	40.3 Ambient spaces of modular symbols
		An ambient space of modular symbols for a congruence subgroup of SL_2(Z).
		The boundary map to the corresponding space of boundary modular symbols.
		Returns a space of modular symbols with the same defining properties (weight, sign, etc.) as this space except with the level N. For example, if self is the space of modular symbols of weight 2 for Gamma_0(22), and level is 11, then this function returns modular symbols of weight 2 for Gamma_0(11).
	modular.math.washington.edu /SAGE/doc/html/ref/module-sage.modular.modsym.ambient.html (1883 words)

	Max (Site not responding. Last check: 2007-10-28)
		Each space's hash table has KEYs for the addresses in the space, and the VALUEs associated with those KEYs can be used for storing implementation information for the addresses in the space.
		In this case, the space is functions, and the implementation of a function is its definition (a hash table mapping arguments to results).
		Now, the space's hash table is stored in a hash table called sos (for space of spaces), looked up by the space's address.
	lists.tunes.org /archives/max/2003/000007.html (550 words)

	Graded vector space - Wikipedia, the free encyclopedia
		In mathematics, a graded vector space is a vector space with an extra piece of structure, known as a grading.
		For example the set of all polynomials in one variable form a graded vector space, where the homogeneous elements of degree n are exactly the polynomials of degree n.
		Then the vector space L(V,W) of graded linear maps is itself an M×N-graded vector space, where M×N is the Cartesian product, since for each choice of homogeneous subspace in the domain, the map may choose a different range homogeneous subspace in the codomain.
	en.wikipedia.org /wiki/Graded_vector_space (515 words)

	Maps between Schemes
		The codomain of the new map is considered to be the scheme Y which must either contain the codomain of f, or lie in that codomain and satisfy f(X) subset Y. Basic Attributes
		The automorphism of the affine space A that permutes its coordinates according to the permutation g.
		The automorphism group of the projective space P together with a map from this group to the set of automorphisms of P, that is, the parent of such automorphisms.
	www.umich.edu /~gpcc/scs/magma/text1020.htm (5798 words)

	topology
		A topological space is a set X together with a collection of subsets OS the members of which are called open, with the property that (i) the union of an arbitrary collection of open sets is open, and (ii) the intersection of a finite collection of open sets is open.
		A topological space is called metric when there is a distance function determining the topology (i.e., open balls for the metric are open sets, and conversely, if a point x lies in an open set U then for some positive e the ball with radius e around x is contained in U.
		We learnt that, for metric spaces, sequential convergence was adequate to describe the topology of such spaces (in the sense that the basic primitives of `open set', `neighbourhood', `closure' etc. could be fully characterised in terms of sequential convergence).
	www.physicsarchives.com /topology.htm (5450 words)

	If Only Darwinists Scrutinized Their Own Theory
		For a deterministic process that maps domain to codomain, any probability on the codomain is a probability pushed forward from the domain (this is standard probability and ergodic theory).
		The processes that connect domain to codomain, insofar as they have any physical significance, must be identified (by scientific investigation) without regard to the actual events in either but solely on the basis of correlations between the two.
		This is why I continue to maintain that interpreting the negative logarithm to the base 2 of a probability is properly thought of as the average number of bits required to specify an event or outcome of that probability (Erik thinks that average number of bits applies to outcomes but not to events).
	www.designinference.com /documents/2002.08.Erik_Response.htm (4907 words)

	codomain - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "codomain" is defined.
		Codomain : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include codomain: codomain space, function codomain
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=codomain (106 words)

	sage.modular.modsym.ambient.ModularSymbolsAmbient
		An ambient space of modular symbols for a congruence subgroup of SL_2(Z).
		For example, decomposing a simple ambient space yields a single factor, and that factor is not an ambient space.
		Returns a space of modular symbols with the same defining properties (weight, sign, etc.) as this space except with the level N. For example, if self is the space of modular symbols of weight 2 for Gamma_0(22), and level is 11, then this function returns modular symbols of weight 2 for Gamma_0(11).
	modular.fas.harvard.edu /sage/api/html/private/sage.modular.modsym.ambient.ModularSymbolsAmbient-class.html (1759 words)

	[No title]
		Spaces that have infinite or very large cardinalities are things that we may hope to denote or to mention in formal terms, even if many times we only wave our hands at them, but we do not come close to touching them the way that we can manage and manipulate finitary signs.
		In the TLC example, the "model space" is the universe of discourse A% = [!A!] = [a_1,..., a_25] that combines the positions of A with the propositions of A^ = (A -> B).
		The "syntactic space" is the formal language L = L(!A!) c (!A! of well-formed strings in the Cactus Language, or pick your own favorite language for the task, that we may variously describe as "expressions", "formulas", "sentences", "terms", "wffs", or whatever fits the moment.
	stderr.org /pipermail/inquiry/2003-June.txt (6755 words)

	Course Syllabus - Lee College (Site not responding. Last check: 2007-10-28)
		To determine if a subset of a vector space along with the inherited operations is a subspace.
		To determine the dimension of a vector space.
		Determine if a given set of vectors in a vector space is a basis for the space.
	www.lee.edu /syllabus_descr.asp?CRSE_ID=001836 (779 words)

	Orðasafn: R (Site not responding. Last check: 2007-10-28)
		2 (codomain of a mapping) bakmengi, = codomain 1, = latent range 2, = potential range, = target 2, = target set.
		4 (of a morphism) bakhlutur, = codomain 2, = range carrier 2, = target 3.
		real analytic space raunfágað rúm, = analytic space 2.
	www.hi.is /~mmh/ord/safn/safnR.html (2382 words)

	What are Sheets?
		A sheet is a representation of a continuous partial function between two spaces which are locally like either (a) n-dimensional Euclidean space or (b) an n-dimensional integer grid.
		The codomain values may be angles, which form a circular space.
		The dimensions of the codomain can be limited to 3D (or perhaps 4D) because of the homogeneity assumption built into the definition of sheets.
	www.cs.hmc.edu /~fleck/envision/language-design/what-are-sheets.html (2341 words)

	Differential Equations and Linear Algebra Chapter 25 -- True or False
		The set of outputs from a function is called the codomain.
		The image of a linear transformation is a subspace of the codomain vector space.
		The dimension of the image of a linear transformation T is called its codomain.
	cwx.prenhall.com /bookbind/pubbooks/farlow/chapter25/truefalse1/deluxe-content.html (88 words)

	[No title]
		The {\tt Hom} command creates the finite-rank free abelian group of homomorphisms from $A$ to $B$, or with a third optional argument, the vector space of homomorphisms in the category of abelian varieties up to isogeny.
		The {\tt FieldOfDefinition} is some field that all the homomorphisms in the Hom space are defined over, but it is not guaranteed to be minimal.
		The {\tt Discriminant} command computes the discriminant of the trace pairing on a Hom space.
	modular.fas.harvard.edu /tables/magma_packages/ModAbVar/homspace.m (1665 words)

	The Convex Basis of the Left Null Space of the Stoichiometric Matrix Leads to the Definition of Metabolically ...
		Each two subspaces in the domain (i.e., the null space and row space) and codomain (i.e., the left null space and column space) form orthogonal pairs with one another.
		space for this transformation is three-dimensional and is spanned
		The concentration solution space is the solid line shown in the two spaces.
	www.biophysj.org /cgi/content/full/85/1/16 (4365 words)

	Section 1 (Site not responding. Last check: 2007-10-28)
		Since there are two basis vectors, the dimension of the null space is 2.
		, or equivalently it is the dimension of the column space of
		is the zero operator and the null space of this operator is all of
	www-math.cudenver.edu /~rrosterm/lins05_6sol/node1.html (475 words)

	quiz14ans (Site not responding. Last check: 2007-10-28)
		The number of points possible for each question is indicated in square brackets - the total number of points on the quiz is 30, and you will have exactly 20 minutes to complete this quiz.
		The CoDomain: The codomain is the list of all possible sums of these pairs of elements from the set of chosen integers.
		The Function that Maps this domain to codomain: Each pair of integers maps to one and only one element in the codomain based on the value of the sum of the two elements in its pair - since the codomain was built specifically for this purpose, it is a total function.
	www.cs.umd.edu /class/fall2004/cmsc250/quiz/quiz14ans (432 words)

	[No title]
		If f:X --> Y, where X is any topological space but Y is a metric space, then the set of continuity points of f is a G-delta.
		If X is a topological space containing two disjoint dense > subsets S and T, then every G-delta set in X is the set of continuity > points of some function f:X --> R. By the way, assuming the axiom of choice, every metric space without isolated points satisfies the hypothesis of the theorem.
		For "metric space without isolated points" read "topological space in which every point has a countable neighborhood base and no one-point set is open".
	www.math.niu.edu /~rusin/known-math/00_incoming/gdelta (622 words)

	Papers - DSL 97
		To avoid wasting scarce space, image values are typically stored as packed bytes, both in memory and in disk files, even though they are conceptually real numbers.
		For the codomain, computer vision programmers are forced to choose between two bad options: discrete integers with an appropriate precision or continuous reals with an inappropriately high precision (thus wasting memory).
		For example, circular codomain values are reduced to the right range using modular arithmetic, whereas linear codomain values are approximated with the closest value in the range.
	www.usenix.org /publications/library/proceedings/dsl97/full_papers/stevenson/stevenson_html/stevenson.html (7968 words)

	Domain (mathematics)
		domain of f, and Y, the set of possible output values, is called the codomain.
		Sometimes the codomain is incorrectly called the range because of a failure to distinguish between possible and actual values.
		A well-defined function must map every element of the domain to an element of its codomain.
	www.danceage.com /biography/sdmc_Codomain_space (375 words)

	Homomorphisms
		Suppose H is a matrix module whose elements have domain A and codomain B.
		Note also that in this case the domain and codomains of H' are the generic R-spaces (tuple modules) corresponding to A (of dimension d) and B (of dimension e).
		The codomain N of the homomorphism a belonging to Hom(M, N).
	www.umich.edu /~gpcc/scs/magma/text787.htm (1723 words)

	lins05finsol (Site not responding. Last check: 2007-10-28)
		Solution: The rank of a matrix is the dimension of the column space.
		Solution: A map is one-to-one if and only if the dimension of its null space is zero.
		A map is onto if and only if the its range equals to codomain.
	www-math.cudenver.edu /~rrosterm/lins05finsol/lins05finsol.html (363 words)

	Outline
		It is assumed students have already seen that the row space and null space are orthogonal complements.
		The green, brown, and wheat vectors are all mapped to the same vector in the column space.
		Part Two would be to repeat this, but with a row space and null space that are different from the x- and y-axes.
	euler.slu.edu /PREP05/DH-decompRowandNullD.mw (552 words)

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