
	Where results make sense

Topic: Linear span

Related Topics

Basis (linear algebra)

Vector space

Hamel dimension

	PlanetMath: span
		Span is both a noun and a verb; a set of vectors can span a vector space, and a vector can be in the span of a set of vectors.
		To see whether a set of vectors spans a vector space, you need to check that there are at least as many linearly independent vectors as the dimension of the space.
		This is version 17 of span, born on 2001-11-13, modified 2008-05-26.
	planetmath.org /encyclopedia/LinearSpan.html (300 words)

	Linear span
		In the mathematical subfield of linear algebra, the linear span, also called the linear hull, of a set of vectors in a vector space is the intersection of all subspaces containing that set.
		The linear span of a set of vectors is therefore a vector space.
		Another spanning set for the same space is given by {(1,2,3), (0,1,2), (â’1,1/2,3), (1,1,1)}, but this set is not a basis, because it is linearly dependent.
	www.algebra.com /algebra/college/linear/Linear_span.wikipedia (471 words)

	Linearly Independent Sets of Vectors
		Note that the first and last linear combinations yield the same vector (0,0), even though the coefficients are not the same.
		Linear dependence of a set of two or more vectors means that at least one of the vectors in the set can be written as a linear combination of the others.
		Linear combinations in complex vector spaces have important applications, as the next examples illustrate.
	distance-ed.math.tamu.edu /Math640/chapter3/node9.html (877 words)

	Linear span - Wikipedia, the free encyclopedia
		In the mathematical subfield of linear algebra, the linear span, also called the linear hull, of a set of vectors in a vector space is the intersection of all subspaces containing that set.
		A spanning set is not necessarily a basis for S as the spanning vectors need not be linearly independent.
		The span of S may also be defned as the collection of all finite linear combinations of the elements of S.
	en.wikipedia.org /wiki/Linear_span (412 words)

	Linear span (Site not responding. Last check: )
		can be written as a linear combination of (finitely many) elements from
		A spanning set that is also linearly independent is a basis.
		Another spanning set for the same space is given by {(1,2,3), (0,1,2), (−1,1/2,3), (1,1,1)}, but this set is not a basis, because it is linearly dependent.
	bopedia.com /en/wikipedia/l/li/linear_span.html (118 words)

	No Title (Site not responding. Last check: )
		A linear combination of vectors is a sum of scalar multiples of the vectors.
		A linear system is just a vector equation where the left-hand side of the equation is a linear combination of some vectors with the unknowns for the system used as scalar multipliers.
		is in the span of the columns of A.
	www.sci.wsu.edu /math/faculty/genz/220v/lessons/l02/l02.html (304 words)

	Span -- Recommendations and Resources (Site not responding. Last check: )
		This page (span) should really be a subpage under linear algebra or vector space, since it is a restricted technical definition which meaningless out of context (critical in context though).---- Span occurs not as a separate page but as an alternate word for "generate" on the Linear Algebra page under Generating a Vector Space.
		In the mathematical subfield of linear algebra, the linear span of a set of vectors is the set of all linear combinations of the vectors.
		The ''linear span'' of a set of vectors is a therefore a vector space but unlike a basis the vectors need not be linearly independent.
	www.becomingapediatrician.com /health/137/span.html (1562 words)

	Review of Chapters 1 and 2
		If the linear system is given as a coefficient matrix A and a vector b, be able to get to the augmented matrix (so you can proceed to solve the system).
		Linear dependence of a set of vectors is a sign that someone is not contributing a dimension to the span.
		Geometrically, this linear combination must be unique because: The set of column vectors is linearly independent since, in a way, each column vector adds something to the span which the other vectors do not possess.
	www.math.uiuc.edu /~johnmaki/ch2review.html (1261 words)

	Publications of M. Neamtu
		It is also shown that the linear span of the simplex splines contains all algebraic polynomials of degree not exceeding the degree of the splines.
		The linear span of the simplex splines forms a spline space with several interesting properties.
		The new approach gives rise to a natural generalization of univariate splines in that the linear span of this collection of B-splines forms a space which is analogous to the classical univariate splines.
	math.vanderbilt.edu /~neamtu/papers/papers.html (4159 words)

	Chapter 13, Convert Network Configurations
		A303 Convert an Unprotected Point-to-Point or 1+1 Linear ADM to a Two-Fiber BLSR Automatically—Complete as needed.
		(Linear ADM only.) Physically remove the protect fibers from all nodes in the linear ADM; for example, the fiber running from Node 2/Slot 13 to Node 3/Slot 13 (as shown in Figure 13-3) can be removed.
		When upgrading point-to-point or linear ADM circuits to a path protection topology, a traffic hit of greater than 300ms occurs if the "Provision working go and return on primary path" routing option is not checked in the Circuit Attributes pane.
	www.cisco.com /univercd/cc/td/doc/product/ong/15400/r70docs/r70procg/r70upgdn.htm (5628 words)

	[No title]
		Part three provides further finiteness results, including a generalization of the linear system fact that finite realizability is equivalent to the existence of a (high-order) input/output difference equation, and studying the relationship between state- affine realizability and more general realizability of a bounded response.
		It is interesting to remark that, since I in (2.9) is span canonical, it follows that the column space X is isomorphic to Lf (by (1.10), (1.11)).
		The equation is output linear iff br, I =0.
	www.mit.edu /~esontag/FTP_DIR/state-affine-realiz.txt (8139 words)

	Linear Algebra for Informatics
		They are a revised version of the ones used in the 2004-2005 session, which were themselves revised due to changes in the syllabus from the ones used in the 2003-2004 session.
		Linear algebra is the study of vector spaces and linear maps.
		We will discuss subspaces, linear (in)dependence, bases, dimension, linear maps and linear transformations and their relation to matrices, the effect of changing basis, eigenvalues and eigenvectors and diagonalisation.
	xmlearning.maths.ed.ac.uk (171 words)

	[No title]
		Part three provides further finiteness results, including a generalization of the linear system fact that finite realizability is equivalent to the existence of a (high-order) input/output difference equation, and studying the relationship between state- affine realizability and more general realizability of a bounded response.
		It is interesting to remark that, since I in (2.9) is span canonical, it follows that the column space X is isomorphic to Lf (by (1.10), (1.11)).
		The equation is output linear iff br, I =0.
	www.math.rutgers.edu /~sontag/FTP_DIR/state-affine-realiz.txt (8139 words)

	Linear Algebra: Linear Combinations and Span - CliffsNotes
		spanned by the vectors i =; (1, 0) and j = (0, 1) is all of R
		That is, if any one of the vectors in a given collection is a linear combination of the others, then it can be discarded without affecting the span.
		Therefore, to arrive at the most “efficient” spanning set, seek out and eliminate any vectors that depend on (that is, can be written as a linear combination of) the others.
	www.cliffsnotes.com /WileyCDA/CliffsReviewTopic/Linear-Combinations-and-Span.topicArticleId-20807,articleId-20788.html (416 words)

	Chapter 12, Convert Network Configurations
		F78 Convert a Point-to-Point or Linear ADM (LMSP) to a Two-Fiber MS-SPRing—Complete as needed.
		Span ring switches are graphically displayed on the span with the letters "L" for lockout ring, "F" for Force ring, "M" for manual ring, and "E" for Exercise ring.
		Also verify that the span lines between the nodes where the manual switch was invoked turn purple, and that the span lines between all other nodes turn green on the network view map.
	www.cisco.com /univercd/cc/td/doc/product/ong/600_sdh/sdh60014/procer14/614pupgd.htm (2539 words)

	Basis (linear algebra) - Wikipedia, the free encyclopedia
		In linear algebra, a basis is a set of vectors that, in a linear combination, can represent every vector in a given vector space.
		A basis B of a vector space V is a linearly independent subset of V that spans (or generates) V.
		For a given vector, the corresponding coefficients in the linear combination are the coordinates of the vector relative to the basis.
	en.wikipedia.org /wiki/Basis_(linear_algebra) (1424 words)

	Linear Independence and Span
		Span(S) If so, then one of the vectors can be written as a linear combination of the others.
		There is another way of checking that a set of vectors are linearly dependent.
		is a nontrivial linear combination of vectors in
	ltcconline.net /greenl/courses/203/Vectors/linIndSpan.htm (214 words)

	Linear Algebra -- Exam 1 Review (Site not responding. Last check: )
		One question this time may consist of several ``true - false'' questions where you must either give a short proof (if you think the statement is true), or a counterexample (if you think the statement is false).
		Linear combinations and the linear span of a set of vectors
		The span of any set S in a vector space V is a vector subspace of V.
	math.holycross.edu /~little/LA04/LARev1.html (322 words)

	Linear Complexity: A Literature Survey
		But linear complexity is the size of a LFSR "processor" to produce a sequence, and there is an algorithm (Berlekamp-Massey) to measure the LC.
		Theory: Chan and Games: Linear complexity is generally a measure of linear span, related to quadratic span, which can be unexpectedly very much smaller than the linear value.
		This arrangement generates keystreams of large linear complexities, however, the statistics of these keystreams is hard to control.
	www.ciphersbyritter.com /RES/LINCOMPL.HTM (2349 words)

	Teaching Linear Algebra
		Margaret Wright in "Linear Algebra for Computer Science Students" finds that most of her coworkers at ATandT Bell Laboratories use linear algebra and describes what she sees as the important topics for computer science majors.
		Gerald Porter in "Writing About Linear Algebra: Report on an Experiment" talks about a linear algebra course for non-mathematics majors in which he had the students write a ten page chapter to supplement the text material on subspaces, spanning sets, basis and dimension, lines, planes and hyperplanes.
		Again, this is a case of linear algebra simplifying the work even though it is not, strictly speaking, needed.
	www.maa.org /reviews/linearalg.html (1787 words)

	[No title]
		Definition 1 We say the vector w from the vector space V is a linear combination of the vectors
		So, we can see that the null space we were looking at above is in fact all the linear combinations of the vector (7,1). It may seem strange to talk about linear combinations of a single vector since that is really scalar multiplication, but we can think of it as that if we need to.
		w is not a linear combination of the two vectors.
	tutorial.math.lamar.edu /classes/linalg/Span.aspx (689 words)

	Linear Algebra -- Final Exam Review
		Linear dependence and independence (know the definitions and how to show whether a set is linearly independent or not)
		Reduction to echelon form as a method for solving systems of linear equations and inverting matrices.
		Every homogeneous system of 3 linear equations in 4 variables has a non-zero solution.
	math.holycross.edu /~little/LA04/FRev.html (865 words)

	Linear Algebra: A Basis for a Vector Space - CliffsNotes
		Since a basis must span V, every vector v in V can be written in at least one way as a linear combination of the vectors in B.
		This expression is a linear combination of the basis vectors that gives the zero vector.
		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 (1581 words)

	[No title]
		In this section we’re going to take a look at an important idea in the study of vector spaces. We will also be drawing heavily on the ideas from the previous two sections and so make sure that you are comfortable with the ideas of span and linear independence.
		If this system has only the trivial solution the vectors will be linearly independent and if it has solutions other than the trivial solution then the vectors will be linearly dependent.
		Example 1(c) from the section on Linear Independence we saw that these vectors are linearly independent.
	tutorial.math.lamar.edu /classes/linalg/basis.aspx (828 words)

Try your search on: Qwika (all wikis)