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Topic: Zero vector

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vector space

vector spatial

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vector graphics

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normed vector space

vector bundle

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vector biology

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	Vector space - Wikipedia, the free encyclopedia
		Vector spaces are the basic objects of study in linear algebra, and are used throughout mathematics, the sciences, 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 which 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 (1469 words)

	Normed vector space - Wikipedia, the free encyclopedia
		A semi normed vector space is a pair (V,p) where V is a vector space and p a semi norm on V.
		A surjective isometry between the normed vector spaces V and W is called a isometric isomorphism, and V and W are called isometrically isomorphic.
		The definition of many normed spaces (in particular, Banach spaces) involves a seminorm defined on a vector space and then the normed space is defined as the quotient space by the subspace of elements of seminorm zero.
	en.wikipedia.org /wiki/Normed_vector_space (890 words)

	PlanetMath: zero vector space
		Every vector space has a zero vector space as a vector subspace.
		Any linear map defined on a zero vector space is the zero map.
		This is version 3 of zero vector space, born on 2003-10-31, modified 2004-02-13.
	planetmath.org /encyclopedia/ZeroVectorSpace.html (98 words)

	400.00 SYSTEM
		Zero pulsation in the vector equilibrium is the nearest approach we will ever know to eternity and god: the zerophase of conceptual integrity inherent in the positive and negative asymmetries that propagate the differentials of consciousness.
		Vector equilibria in isotropic vector matrixes produce the discontinuity of particles, while the vector-weaving around the VE nuclei produce the continuity of wave phenomena.
		The vector equilibrium is the nothingness phase of all states of physical Universe: it is the generalization of nothingness, within which generalization the absolute vacuum is a special case event in the gaseous state.
	www.rwgrayprojects.com /synergetics/s04/p4000.html (1863 words)

	PlanetMath: vector space
		is the zero vector in a vector space
		This is version 12 of vector space, born on 2001-10-19, modified 2006-07-22.
		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)

	Double-Valued Vectors ( vector )
		An instance of data type vector is a vector of variables of type double.
		creates an instance v of type vector; v is initialized to the zero vector of dimension d.
		Be aware that the operations on vectors and matrices incur rounding errors and hence are not completely reliable.
	www.algorithmic-solutions.info /leda_manual/vector.html (317 words)

	Zero Vector - 3D Geometric Forecasting (Site not responding. Last check: 2007-10-23)
		Zero Vector is a proprietary technique based on the latest scientific advancements in Fractal Geometry, Chaos Theory, and Complex Systems theory.
		Zero Vector is based on a FUNDAMENTAL 3 DIMENSIONAL PATTERN that we believe is just as important and consistent as the Elliot Wave fractal pattern.
		Zero Vector is not based on the work of William D. Gann, a very successful mathematician and stockbroker in the 1900's.
	www.zerovector.com /page/page/864826.htm (1410 words)

	Insert Zero (Communications Blockset)
		The Insert Zero block constructs an output vector by inserting zeros among the elements of the input vector.
		If the input signal is sample-based, then the input vector length must equal the number of 1s in the Insert zero vector parameter.
		If the input vector length is greater than the number of 1s in the Insert zero vector parameter, then the block repeats the insertion pattern until it has placed all input elements in the output vector.
	www-rohan.sdsu.edu /doc/matlab/toolbox/commblks/ref/insertzero.html (307 words)

	Is zero speed a constant speed? \| Ask MetaFilter (Site not responding. Last check: 2007-10-23)
		A vector space is a set over a field (such as the real numbers) that has two operations (call them + and *) and a number of properties, but the important one here is that the space is a commutative group under +.
		In the case at hand, "a vector has a magnitude and a direction" would work perfectly well for many things; it would be a little more subtle than the definition most people like (which is better encoded by things like (x,y,z)) because there'd be many different flavors of "zero vector".
		Similarly, if you can't regard a velocity of zero as constant [even when the function describing the velocity, and the derivative of that function which proves that the velocity is constant, follow all of the rules of calculus, arithmetic, etc], you're choosing to disagree with the way math works.
	ask.metafilter.com /mefi/17787 (5568 words)

	The Tom Bearden Website
		It is a square of the amplitude, hence for the vector part of a wave, it is directly proportional to the energy density of the vacuum, as a function of time, at the particular position.
		Evidently, Bearden's idea is that each physical field vector v should be replaced with a quaternion q = (−v²,v) (we have added a minus sign to the scalar part due to our preceeding remark), where the scalar part is proportional to the energy density of the vector field shown in the vector part.
		Therefore destructive interference cannot be used as an example of vector zero resultant fields in the sense of quaternions.
	www.mathematik.tu-darmstadt.de /~bruhn/Bearden-ch4.htm (906 words)

	Zero Vector as Orthogonal (Site not responding. Last check: 2007-10-23)
		The dot product of the zero vector with the given vector is zero, so the zero vector must be orthogonal to the given vector.
		This is OK. Math books often use the fact that the zero vector is orthogonal to every vector (of the same type).
		Of course, the length of the zero vector is zero, so it is not a unit normal.
	chortle.ccsu.ctstateu.edu /VectorLessons/vch08/vch08_12.html (182 words)

	Rational Vectors ( rat_vector )
		An instance of data type rat_vector is a vector of rational numbers.
		The main difference between position vectors and free vectors is their behavior under affine transformations, e.g., free vectors are invariant under translations.
		Vectors are implemented by arrays of integers as an item type.
	www.mpi-sb.mpg.de /LEDA/MANUAL/rat_vector.html (610 words)

	Zero Vector
		The zero vector is that (unique) element 0, for which 0+x=x for all vectors x in your vector space.
		vector quantities in the physics/mechanics usage of the term may be usefully said to have directions, but a vector quantity with no magnitude isn't acting in any direction really.
		A vector is something abstract.It is an element of a set.Therefore i could use any graphical symbol to "picture" it on the paper or in my mind.Even a circle or a sphere.
	www.physicsforums.com /showthread.php?threadid=78856 (940 words)

	Algorithms and Special Topics
		Direct conversion from vector shorts and vector chars is possible with this general method, and in many cases can be faster than the more standard method.
		The central problem facing would-be vectorizers for this task, is that using the traditional algorithm, rows of matrix A are multiplied by columns of matrix B, which may mean transposing matrix B. In addition you then have to sum across the result, which is not very efficient.
		Commonly when working with constant terms in vector code, it is desirable to be able to load a scalar and splat it across a register.
	developer.apple.com /hardware/ve/algorithms.html (3278 words)

	Vector (Java 2 Platform SE v1.4.2)
		Constructs an empty vector with the specified initial capacity and with its capacity increment equal to zero.
		Trims the capacity of this vector to be the vector's current size.
		The capacity of the vector is the length of this array buffer, and is at least large enough to contain all the vector's elements.
	java.sun.com /j2se/1.4.2/docs/api/java/util/Vector.html (3241 words)

	GRAD
		Since the class Vector has no global attributes, VECTOR.py is a file of zero length and _GLOBAL_.py is just a skeleton.
		The Vector istream and ostream operators are global.
		Note the class attributes zero, unit_x, unit_y and unit_z being handled by the __getattr__ and __setattr__ methods.
	www.python.org /workshops/1996-11/papers/GRAD/html/GRADappendix.html (983 words)

	Vector Spaces
		It is important that a real vector space consist of the set of vectors and the two operations with certain properties.
		To show that an object is a vector space, we must show that closure for both operations holds [parts (b) and (c) of the definition] and that properties 1 through 8 hold.
		When you are working with complex vector spaces, it is important to remember that the vectors can be constructed by using complex numbers and that the scalars for scalar multiplication can be any complex number.
	distance-ed.math.tamu.edu /Math640/chapter3/node4.html (1048 words)

	KVR : White Noise Audio Zero Vector
		Zero Vector is a unique combination of Virtual Analog synth, ROM Wavetable Synth, and Vector Synth.
		In all, Zero Vector is a major synth with tons of capabiliies and tons of personality.
		Zero Vector isn't cheap, but considering the league it is playing in, the immense universality and its sheer quality, it is very reasonable priced.
	www.kvraudio.com /get/1261.html (2330 words)

	ZERO - initialize a B vector to some value. (Site not responding. Last check: 2007-10-23)
		ZERO - initialize a B vector to some value.
		is the value to which the elements of the vector are to be initialized.
		ZERO initializes the contents of a vector to the specified value.
	www.thinkage.on.ca /english/gcos/expl/b/lib/zero.html (77 words)

	[ref] 56 Vector Spaces
		Vector spaces are free left modules over a field.
		A vector space is Gaussian if it allows Gaussian elimination; this is used for row vector spaces and matrix vector spaces.
		The only thing they have in common is that one can ask both for their basis vectors and for the coefficients of a given vector.
	sylow.slu.edu /gap/htm/ref/CHAP056.htm (2396 words)

	VECTOR MATHEMATICS HAS A FUNDAMENTAL PROBLEM (Site not responding. Last check: 2007-10-23)
		Obviously, in the physical case vector zero summations may materially differ, both in the pattern of stress and the magnitude of stress.
		(1) the "potential" of a vector zero must be taken into account, such as is represented by the sum of the squares of the magnitudes of its vector components.
		Here we still are considering only a special case where all vector zero summations represent EM force field energy locked in a gravitational potential, or gravitational force field energy locked inside the EM potentials.
	www.rumormillnews.com /cgi-bin/archive.cgi?noframes;read=72036 (713 words)

	[ref] 58 Vector Spaces
		The characteristic (see Characteristic) of a vector space is equal to the characteristic of its left acting domain.
		Storing the module allows one for example to deal with bases whose basis vectors have not yet been computed yet (see Basis); furthermore, in some cases it is convenient to test membership of a vector in the module before computing coefficients w.r.t.
		Examples of such vector spaces are vector spaces of field elements (but not the fields themselves) and non-Gaussian row and matrix spaces (see IsGaussianSpace).
	www.math.temple.edu /computing/gap/ref/CHAP058.htm (3619 words)

	TEMP\4_4
		At the same time, the zero value of the plane coefficient may induce a non-zero value of the vector of accelerations.
		in which the vector of the main acceleration is represented by an infinitesimal quantity, i.e., is equal to zero.
		This means that the vector of the sum angular velocity is perpendicular to one or two coordinate axes.
	www.math.rsu.ru /zimin/4_4.html (1826 words)

	The Tom Bearden Website
		The vector sum of these two virtual forces in the vacuum is a zero vector; however, the two taken together represent a stress in the local energy density of vacuum.
		And when two vectors multiply to provide a zero vector resultant, corresponding quaternions may yield a scalar term that is equal to the product of the magnitudes of the two vectors.
		In the vector approach, the stress of the medium is entirely lost when the two vectors sum or multiply to a zero resultant.
	www.cheniere.org /books/aids/ch4.htm (5068 words)

	Linear Algebra (Math 2318) - Vector Spaces - Vector Spaces (Site not responding. Last check: 2007-10-23)
		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.
		that are NOT vector spaces so hopefully it is clear that there are sets out there that aren’t vector spaces. In each case we had to change the definition of scalar multiplication or addition to make the set fail to be a vector space.
		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 /AllBrowsers/2318/VectorSpaces.asp (1897 words)

	MUG: zero times vector becomes a number (26.3.99) (Site not responding. Last check: 2007-10-23)
		Using evalm, a scalar times a vector is a vector, unless the scalar is zero, when the result is not the zero vector, but the number zero.
		This causes problems with things like pointplot3d which wants a list of vectors and chokes if zero is put in.
		Maple-operations which are for the use with vectors should be prepeared for the use with 0, too.
	www.math.rwth-aachen.de /mapleAnswers/html/738.html (231 words)

	Eigenvalues and Eigenvectors
		Moreover, we require that an eigenvector be a non-zero vector, in other words, an eigenvector can not be the zero vector.
		The vector obtained in step 4 is an approximate eigenvector corresponding to the dominant eigenvalue.
		We are allowed to do this because, as Remark 29 states, we can divide by any element in the vector as long as we are consistent with our choice throughout the problem.
	ceee.rice.edu /Books/LA/eigen (2757 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Vector(); // n-dimensional zero vector, n >= 0.
		Vector(int n); // n-dimensional vector with components array as components.
		Vector(double* components, int n); // Return zero vector of same dimension as v.
	www.cs.toronto.edu /~gfb/csc270/2000F/A4/soln/Vector.h (133 words)

	dig: vec4 struct Reference
		Return whether this vector is greater than or equal to b in each axis.
		Return whether this vector is greater than b in each axis.
		Return whether this vector is less than or equal to b in each axis.
	www.opend.org /dig/structvec4.html (228 words)

	[No title]
		When applied to n, it represents the zero vector of size n (in the terminology of linalg3; dimension n in some terminology).
		When applied to n and c, it represents the constant (row) vector (so vector as defined in linalg2), so size (dimension) n all of whose components have the value c.
		The sparse symbol is a constructor for sparse vectors.
	www.win.tue.nl /~amc/oz/om/cds/linalg4vec.ocd (337 words)

	Linear algebra notes
		Possibly this is the only vector in the space, in which case the space is trivial.
		The zero vector is not a nontrivial linear combination of the vectors
		If a linearly independent set also spans the vector space it is in, then it is called a basis of that space.
	www.math.metu.edu.tr /~dpierce/linear_algebra/spaces.html (608 words)

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