
	Where results make sense

Topic: Vector space example 1

Related Topics

Vector space

Vector space example 3

Normed vector space

Vector space example 2

Differential topology

List of mathematical proofs

History of South Africa

Cyrenaica

Vector space

Kerim Tekin

Loa

	PlanetMath: vector
		Indeed, it is customary to depict a physical vector as an arrow.
		An abstract vector is an element of a vector space.
		Essentially, given a finite dimensional abstract vector space, a choice of a coordinate frame (which is really the same thing as a basis) sets up a linear bijection between the abstract vectors and list vectors, and makes it possible to represent the one in terms of the other.
	planetmath.org /encyclopedia/Vector2.html (1187 words)

	Vector space
		The fundamental concept in linear algebra is that of a vector space or linear space.
		Given two vector spaces V and W over the same field, one can define linear transformations or "linear maps" from V to W. These are maps from V to W which are compatible with the relevant structure, i.e.
		In abstract algebra, the concept of a vector space is generalized to modules by replacing the underlying field F by a ring and retaining the above 10 axioms.
	www.ebroadcast.com.au /lookup/encyclopedia/ve/VectorSpaces.html (769 words)

	Vector space example 3: Definition and Links by Encyclopedian.com
		...norm, is called...that of a vector space or linear space.
		So Example I would be denoted R 1xn...M is a vector space over C and we denote this as C mxn.
		...The dimension of a vector space V is the cardinality (i.e.
	www.encyclopedian.com /ve/Vector-space-example-3.html (649 words)

	Vector space (Site not responding. Last check: 2007-11-06)
		Simply put, a vector space over a field F is just an F-module.
		Given a vector space V, any nonempty subset W of V which is closed under addition and scalar multiplication is called a subspace of V. It is easy to see that subspaces of V are vector spaces (over the same field) in their own right.
		Given a translationally invariant and rescaling invariant topology over a vector space (preferably infinite-dimensional), the sum of an infinite sequence of vectors can be defined as the topological limit, if it exists.
	bopedia.com /en/wikipedia/v/ve/vector_space_1.html (826 words)

	PlanetMath: vector space
		This is version 12 of vector space, born on 2001-10-19, modified 2006-07-22.
		What vector space is not a metric space?
		Hungerford's _Algebra_ defines vector spaces as unitary modules over division rings, which means funky, noncommutative things can happen (you can have a "left" vector space which isn't a "right" vector space, for example).
	planetmath.org /encyclopedia/VectorSpace.html (290 words)

	Vector space - Wikipedia, the free encyclopedia
		Vector spaces are the basic objects of study in linear algebra, and are used throughout mathematics, science, and engineering.
		Vectors in these spaces are ordered pairs or triples of real numbers, and are often represented as geometric vectors which are quantities with a magnitude and a direction, usually depicted as arrows.
		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.
	en.wikipedia.org /wiki/Vector_space (1598 words)

	Vector Spaces
		One of the fundamental concepts of linear algebra is the concept of vector space.
		In analysis the notion ``linear space'' is used unstead of the notion ``vector space''.
		Instead of the notion ``vector space'' we shall use the abbreviative ``space''.
	www.cs.ut.ee /~toomas_l/linalg/lin1/node5.html (382 words)

	Vector Space
		A Vector Space is formed from two sets, the vectors and the scalars, which are their coefficients.
		Vectors form an abelian group with respect to addition, which is to say that sums are closed, associative, commutative, and that there are negatives and a zero.
		For example, might be a vector space of polynomials.
	www.lycos.com /info/vector-space.html (259 words)

	Vector Spaces (over a field). Modules (over a ring). Algebras... - Numericana
		A Banach space is a normed vector space which is complete (which is to say that every Cauchy sequence in it converges).
		A module obeys the same basic rules as a vector space, but its scalars are only required to form a ring; a nonzero scalar need not have a reciprocal...
		The octonions are an example of a non-associative algebra.
	home.att.net /~numericana/answer/vectors.htm (783 words)

	Vector - GPWiki
		Vectors are a pretty essential part of graphics, physics, game logic and even a lot of AI for games.
		The meaning of adding vector A and vector B together is that the new vector represents what you get to when you first follow vector A then follow vector B. Negating a vector just changes its direction to be the opposite of the original direction, and leaves the length the same.
		If two vectors lie in a plane (any two vectors that do not point in the same or opposite direction form a plane), their cross-product is the normal of that plane.
	gpwiki.org /index.php/Math:Vector (1085 words)

	Math Forum - Ask Dr. Math
		I thought that a dual space was when you have a vector space V and you have a transformation L that takes V to another vector space U. And a dual map is a function that assigns U* to a field in V*.
		Any vector parallel or anti-parallel to the z-axis has x=0 and y=0, and thus L maps any vector that points straight up in the +z direction, or straight down in the -z direction, to the zero vector.
		The set of vectors which are orthogonal to all vectors in the x-y plane are all vectors which point straight up in the +z direction or straight down in the -z direction.
	mathforum.org /library/drmath/view/63857.html (1088 words)

	Vector space example 1: Definition and Links by Encyclopedian.com
		So Example I would be denoted R 1xn...we denote this as C mxn.
		So Example I would be denoted R 1xn, or more simply, R n.
		Then V is a Vector Space over R.
	www.encyclopedian.com /ve/Vector-space-example-1.html (508 words)

	State Space Example #1
		The state space representation of a system is one way in which the mathematical model of the system can be expressed.
		The state space model for an nth-order system is a set of n 1st-order differential equations, called the state equations, and a set of p algebraic equations, called the output equations.
		As an example of how the initial conditions cause different outputs for the two models, each model was given an initial state vector consisting of 1 for each element (4 of them for the full-order model, 3 for the reduced-order model).
	ece.gmu.edu /~gbeale/ece_220/state_space_01.html (1804 words)

	1
		In this section we state the axioms of a vector space; discuss the two major types of vector spaces that will be of interest to us, n-dimensional Euclidean space and function spaces; define what is meant by a subspace, and then examine some examples of subspaces.
		III says that addition of vectors is commutative; IV says addition of vectors is associative; V describes 0 as the additive identity for vectors; VI says that any given vector v has an additive inverse w; VII describes various distributive laws for mixes of constants and vectors.
		Definition Let V be a vector space and W be a non-empty subset of V that is a vector space, relative to the operations of vector addition and scalar multiplication defined for V. Then W is called a subspace of V. Theorem 1.
	www.math.ucla.edu /~ronmiech/33a/VecSp_SubSp/VECTORSPACE.html (3008 words)

	[No title]
		A basis of the space of polynomials is: 2 3 4 {1, x, x, x, x,...
		Example 2: Consider all things of the form x x x x c x e Sin[x]+c x e Cos[x]+c e Sin[x]+c e Cos[x] 1 2 3 4 Is this closed under addition?
		The basis of the space V is
	orion.math.iastate.edu /hentzel/class.307.05/Mar.04 (573 words)

	Maths - Vectors - Martin Baker
		As a subset of a matrix (1 by n, or n by 1 matrix).
		Regardless of whether we consider vectors as a special case of matrices, or matrices as vectors of vectors, or if we consider vectors and matrices as different types, using vectors and matrices together is very important.
		An example of this is Einsteinean space-time, space and time dimensions square to different values, if space squares to positive then time squares to negative and visa-versa.
	www.euclideanspace.com /maths/algebra/vectors (1997 words)

	[No title]
		V is called a vector space and the objects in V are called vectors.
		We should now look at some examples of vector spaces and at least a couple of examples of sets that aren’t vector spaces. Some of these will be fairly standard vector spaces while others may seem a little strange at first but are fairly important to other areas of mathematics.
		we would not have a vector space. Next, do not get excited about the definitions of “addition” and “scalar multiplication” here. Even though they are not they are not addition and scalar multiplication as we think of them we are still going to call them the addition and scalar multiplication operations for this vector space.
	tutorial.math.lamar.edu /Classes/LinAlg/VectorSpaces.aspx (1564 words)

	[No title]
		W of a vector space V was a subspace we’d need to show that all 10 of the axioms from the definition of a vector space are valid, however, in reality that doesn’t need to be done.
		Example 1 Determine if the given set is a subspace of the given vector space.
		Example 2 Determine if the given set is a subspace of the given vector space.
	tutorial.math.lamar.edu /Classes/LinAlg/Subspaces.aspx (1189 words)

	Vector Spaces
		In what follows, V will denote a vector space over a field F. I'll show that many of the properties you'd expect vectors to have are true.
		In this case, the zero vector is in W, so the issue isn't settled, and I'll try to check the subspace axioms.
		Since W is not closed under vector addition, it is not a subspace.
	marauder.millersville.edu /~bikenaga/linearalgebra/vectorsp/vectorsp.html (1124 words)

	Examples of vector spaces - Wikipedia, the free encyclopedia
		The space of all functions from X to V is a vector space over F with coordinate-wise addition and multiplication.
		An important example arising in the context of linear algebra itself is the vector space of linear transformations.
		Apart from the trivial case of a zero-dimensional space over any field, a vector space over a field F has a finite number of elements iff F is a finite field and the vector space has a finite dimension.
	en.wikipedia.org /wiki/Examples_of_vector_spaces (1411 words)

	Cascading Style Sheets, level 1
		But, as the example shows, the placement of an element is relative to ancestors and siblings, so these elements' padding and margin properties have an effect on their children.
		For example, by setting the 'float' property of an image to 'left', the image is moved to the left until the margin, padding or border of another block-level element is reached.
		Examples of constraints of the presentation medium are: limited resources (fonts, color) and limited resolution (so margins may not be accurate).
	www.w3.org /TR/REC-CSS1 (15136 words)

	State Space Example
		The state space model for an nth-order system is a set of n 1st-order differential equations, called the state equations, and a set of p algebraic equations, called the output equations.
		As an example of how the initial conditions cause different outputs for the two models, each model was given an initial state vector consisting of 1 for each element (4 of them for the full-order model, 3 for the reduced-order model).
		Obviously, the mode that is missing from the poles of the transfer function is the one which was cancelled by a zero in the original form of the transfer function.
	bass.gmu.edu /ececourses/ece220_320_421/stspacex.html (1794 words)

	Vector Arithmetic
		Since a vector is defined by its magnitude and direction, changing its location in our reference frame without changing its direction or magnitude leaves it the same vector.
		I have already defined the scalar components of a vector as the coordinates of the head of the vector when its tail is at the origin.
		Remember that the sum of two vectors is a vector from the tail of the first to the head of the second.
	www.mcasco.com /p1va.html (1972 words)

	Simple Vector Library (documentation)
		In the expression m * v, v is treated as a column vector; in the expression v * m, it is treated as a row vector.
		Vectors and matrices are parsed in the same format that they are output: vectors are delimited by square brackets, elements separated by white space, and matrices consist of a series of row vectors, again delimited by square brackets.
		In this coordinate system an n-vector is embedded in a (n+1)-dimensional space, e.g., a homogeneous point in 2d is represented by a 3-vector.
	www-2.cs.cmu.edu /~ajw/doc/svl.html (1427 words)

	Abstract linear spaces
		The parallel development in analysis was to move from spaces of concrete objects such as sequence spaces towards abstract linear spaces.
		Bellavitis then defines the 'equipollent sum of line segments' and obtains an 'equipollent calculus' which is essentially a vector space.
		Hamilton represented the complex numbers as a two dimensional vector space over the reals although of course he did not use these general abstract terms.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Abstract_linear_spaces.html (1861 words)

	Space Vector PWM VSI Induction Motor Drive :: Blocks (SimPowerSystems)
		The speed controller, the braking chopper, and the space vector modulator models are specific to the drive library.
		The αβ vector sector is used to find the sector of the αβ plane in which the voltage vector lies.
		The block input is the sector in which the voltage vector lies.
	www.mathworks.com /access/helpdesk/help/toolbox/physmod/powersys/ref/spacevectorpwmvsiinductionmotordrive.html (1603 words)

	Slashdot \| Vector Space Search Engines in Perl
		And the claim that vector search is faster than a database search is true, for as long as you can fit all the document vectors into RAM.
		One example, as you point out, is neglecting to mention practical ways of reducing vector size (number of keywords).
		The simple vector space model is fundamentally flawed for ranking in that it is biased towards returning short documents containing your terms.
	developers.slashdot.org /article.pl?sid=03/02/26/1635254 (2531 words)

	CliffsNotes::Linear Algebra: A Basis for a Vector Space
		Example 6: In, the vectors i and k span a subspace of dimension 2.
		Example 7: The one-element collection { i + j = (1, 1)} is a basis for the 1-dimensional subspace V of R
		If C were a basis, the vector v could be written as a linear combination of the vectors in C in one and only one way.
	www.cliffsnotes.com /WileyCDA/CliffsReviewTopic/A-Basis-for-a-Vector-Space.topicArticleId-20807,articleId-20791.html (1562 words)

	Linear Algebra Webnotes. Part 4.
		The results of the first two are vectors (so we do not escape the set of vectors), the result of the third one is a scalar (not a vector on the plane).
		Any vector space V with a dot product which satisfies properties 1-4 is called a Euclidean vector space.
		Orthogonal vectors in arbitrary Euclidean vector spaces have properties similar to orthogonal vectors on a plane.
	www.sftw.umac.mo /~fstitl/linweb/feb5.html (1576 words)

	Vector Spaces
		This is a vector space as you can check.
		is not a vector space, since property a1 fails.
		Vector spaces enjoy several additional properties that we will later explore.
	www.ltcconline.net /greenl/courses/203/Vectors/vectorSpaces.htm (328 words)

	4Mation Demo - Vector, the RiscOS Drawing Package
		Vector is an advanced object-oriented vector graphics application for Acorn machines and compatibles running RiscOS, mostly compatible with Draw (using the same file format and with a similar user interface) but with many new and powerful features.
		There is not enough space here to describe all of the standard and special objects supported.
		Vector requires a minimum of RiscOS 3 and 2Mb memory, but of course is fully compatible with RiscOS 4, Risc PC and StrongARM.
	www.keelhaul.me.uk /4mation/vector.htm (989 words)

Try your search on: Qwika (all wikis)