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Vector (spatial) - Wikipedia, the free encyclopedia In physics and engineering, a vector is a physical entity which has a magnitude which is a scalar (a physical quantity expressed as the product of a numerical value and a physical unit, not just a number). A spatial vector is a special case of a tensor and is also analogous to a four-vector in relativity (and is sometimes therefore called a three-vector in reference to the three spatial dimensions, although this term also has another meaning for p-vectors of differential geometry). Informally, a vector is a quantity characterized by a magnitude (in mathematics a number, in physics a number times a unit) and a direction, often represented graphically by an arrow. en.wikipedia.org /wiki/Vector_(spatial)   (2838 words)

PlanetMath: vector   (Site not responding. Last check: 2007-10-15) A physical vector (follow the link to a formal definition and in-depth discussion) is a geometric quantity that correspond to a linear displacement. Indeed, it is customary to depict a physical vector as an arrow. 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   (1189 words)

Patent 4620275: Computer system Vector elements are transmitted from memory, either main memory, a physical cache unit or a logical cache through a source bus where the elements are alternately loaded into the vector processing units. A second vector processing unit is connected in parallel with the first vector processing unit for processing vector operands concurrently with the first vector processing unit wherein the vector is transmitted through the source bus and the elements thereof are loaded alternatively in the first and second vector processing units. The physical address is then passed to the main memory 99 where the desired instruction is retrieved, typically within a block of instructions, and passed through the data line 88, the memory control unit 22, line 102, and to the physical cache unit 100. www.freepatentsonline.com /4620275.html   (11811 words)

Patent 4926317: Hierarchical memory system with logical cache, physical cache, and address translation unit for ... Vector elements are transmitted from memory, either main memory (99), a physical cache unit (100) or a logical cache (326) through a source bus (114) where the elements are alternately loaded into the vector processing units (148, 150). The resulting vectors are transmitted through a destination bus (114) to either the physical cache unit (100), the main memory (99), the logical cache (326) or to an input/output processor (54). Physical address B line 122 (11..5) is connected to a buffer 223 which is further connected to the first input of switch 191. www.freepatentsonline.com /4926317.html   (11301 words)

Vector space Article, Vectorspace Information   (Site not responding. Last check: 2007-10-15) This is a generalization of the set of allgeometrical vectors and is used throughout modern mathematics. 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 Vare vector spaces (over the same field) in their own right. The mostbasic physical vector is the displacement vector from point A topoint B (its direction is from A to B and its length is the distance between A and B). www.anoca.org /field/linear/vector_space.html   (1105 words)

PlanetMath: physical vector Finally, we define a physical vector to be an equivalence class of such pairs relative to the just-defined relation. The central weakness of his definition is that he is unwilling to distinguish between physical vectors (quantities) and their representation (lists of numbers). This is version 2 of physical vector, born on 2002-07-24, modified 2002-10-19. planetmath.org /encyclopedia/PhysicalVector.html   (845 words)

More About Celestials Vector 1 spans the spectrum from the realm of quarks to the realm of the entire physical universe. Vector 2 spans the spectrum of organic conscious existence from the micro to the macro. Vectors 1 and 2 are of the exhalation of the living, breathing Wholeness. www.sangres.com /hotp/project/celestials02.htm   (1586 words)

Buckingham Pi theorem - Wikipedia, the free encyclopedia Proofs of the π theorem often begin by considering the space of fundamental and derived physical units as a vector space, with the fundamental units as basis vectors, and with multiplication of physical units as the "vector addition" operation, and raising to powers as the "scalar multiplication" operation. The π-theorem uses linear algebra: the space of all possible physical units can be seen as a vector space over the rational numbers if we represent a unit as the set of exponents needed for the fundamental units (with a power of zero if the particular fundamental unit is not present). Taylor supposed that the description of the process was adequately described by five physical quantities, the time t  since the detonation, the energy E  which is released at a single point in space at detonation, the radius R  of the shock wave at time t , the atmospheric pressure p  and the ambient density ρ. en.wikipedia.org /wiki/Buckingham_Pi_theorem   (946 words)

Field Operators As it is generally known, gradient of a scalar function is a vector the direction of which points the maximum growth of the function and its magnitude is equal to the derivative of that function along that direction. It is a vector which roughly speaking characterizes the vector field as for its charge in space in the plane perpendicular to the "curl" of that vector field. Our vector quantity, then must be thought of as capable of applying a force to each blade of the paddle wheel, the force being proportional to the component of the field normal to the surface of that blade. www.eaeeie.org /theiere/curvilinear/FieldOperators.htm   (2681 words)

DIstributed Vector Architecture   (Site not responding. Last check: 2007-10-15) However, real-life vector applications, which have enormous memory requirements, would not fit in the non-expandable memory of a single integrated device and their performance would be primarily determined by the amount of remote traffic they require. Vector processors of individual nodes cooperate together to work as a single larger vector processor, while the vector application occupies the memory of all nodes. Vector operations on the architectural registers are distributed among the nodes, each of which operates on its assigned elements. www.cs.wisc.edu /~kaxiras/diva.html   (300 words)

The Tom Bearden Website   (Site not responding. Last check: 2007-10-15) In the abstract mathematics, a vector zero summation is made the "absence of all finite vectors". In the physical case, a vector zero summation system of non-zero vectors has a dynamic substructure, and this substructure is an individual. Obviously, in the physical case vector zero summations may materially differ, both in the pattern of stress and the magnitude of stress. www.cheniere.org /books/ferdelance/s8.htm   (545 words)

[No title] Large vector fields, vector fields with wide dynamic ranges in magnitude, and vector fields representing turbulent flows can be difficult to visualize effectively using common techniques such as drawing arrows or other icons at each data point, or drawing streamlines[2]. The vector which describes the velocity of the flow at each point is [dx/dt, dy/dt, dz/dt]T. We transform the vector field to the coordinate system of the curvilinear grid, hereafter called "computational space." The transformation from physical space to computational space is performed by multiplying the physical-space velocity vectors by the inverse Jacobian matrix s.t. The resulting image, which is a visualization of the vector field in computational space (see Figure 3) is then mapped onto the surface in physical space using a standard inverse mapping algorithm, such as that described in [9]. graphics.stanford.edu /papers/flowvis/flowvis.txt   (3186 words)

[No title]   (Site not responding. Last check: 2007-10-15) VECTOR FIELDS AND THE UNITY OFMATHEMATICS AND PHYSICS by Daniel HenryGottlieb Department of Mathematics Purdue University West Lafayette, Indiana 47906 Abstract We give an argument that magnetic monopoles should not exist. The thrust of the argument is that indi* *ces of vector fields are invariants of space-time orientation and of coordinate changes,and t* *hus physical vector fields should preserve indices. The index of any "physical" vector field is invariant under changes of coordinates and orientation of space-time. hopf.math.purdue.edu /Gottlieb/unity.abstract   (452 words)

VECTOR Given two points A and B, is the vector with its base at A and tip at B. Its magnitude is the distance between A and B and its direction is in the direction from A toward B. Equivalent vectors describe the same relationship between different sets of points. spatial vectors that are used by a coordinate system (cs) to describe all other spatial vectors in that system using coordinates. These coordinates may represent a displacement vector, position vector, translation vector etc.The coordinates must be used with an understanding of what they represent and in what reference frame. personal.uncc.edu /jamiller/terms/VECTOR.htm   (453 words)

Vector space at opensource encyclopedia   (Site not responding. Last check: 2007-10-15) 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 two vector spaces V and W over the same field F, 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., they preserve sums and scalar products. The most basic physical vector is the displacement vector from point A to point B (its direction is from A to B and its length is the distance between A and B). wiki.tatet.com /Vector_space.html   (1176 words)

[No title] The curl of E at a point x is the direction (or vector) k such that when you take a little contour around x which normal is k, and you multiply the curl at x by the area inside the contour, you have the circulation of E around this contour. Now remember what question you're asking the paddle-wheel: "What is the curl of the given vector field at the concurrence point of the paddles?" Now be careful: the answer is a 3D vector, which we think of as a "physical vector" or "arrow" originating at the point. The magnitude of the curl vector is proportional to the angular speed of the paddle. www.math.niu.edu /~rusin/known-math/00_incoming/div_grad   (1418 words)

ME210 Weekly Outline Representation of curves and surfaces by writing the position vector of a general point on the curve or on the surface. Derivative of position vector and its geometrical significance (tangent vector to a curve). Physical significance of derivative of position vector (velocity and acceleration). www.me.metu.edu.tr /me210/Outline.htm   (204 words)

13   (Site not responding. Last check: 2007-10-15) We introduced a more abstract discussion of the invariants and transformation laws in a vector space, taking the vector space to be that defined by column vectors, whose entries are a physical vector's components with respect to some set of axes, or ``basis''. The physicality, or invariance of probability amplitudes under basis change (with basis changes often motivated by the physical meaning of measurement), means that the adjoint operation becomes extremely important in QM. Made philosophical comment on how the ``partnering'' we see here, of column vector with row vector, vector with covector, ket with bra, is a structure that recurs throughout math and physics, specifically in quantum mechanics, differential geometry, special and general relativity. www.emory.edu /PHYSICS/Faculty/Benson/320/notes/13/13.html   (621 words)

[No title] Definitions From a mathematical point of view, a vector is an array of 2 or more elements arranged into a row or a column. Since in the calculator vectors are written between brackets [ ], we will choose the notation A = [Ax, Ay, Az] or A = [Ax, Ay, Az], to refer to two- and three-dimensional vectors from now on. The magnitude of a vector A is defined as A =  EMBED Equation.3  . freelance-translator.netfirms.com /Scientific_translation.doc   (631 words)

The Tom Bearden Website Since the spinning electron mass is the "zipper" that makes or comprises the physical vector in the first place, this throttling of the mass flow unzips the E and B vectors, leaving whirling (massless magnetic scalar potential) segments of massless charge flux (massless electrostatic scalar potential). This is a special kind of scalar wave pattern, not a physical or vector wave. (18) All changes to and from a physical vector or scalar system must arise in and come from its own internal substructure, which is zipped to its spinning particle of mass. www.cheniere.org /books/part3/implications.htm   (1316 words)

vector on Encyclopedia.com Many physical quantities are vectors, e.g., force, velocity, and momentum. Vector Vs. Bitmap Intricate illustrations can be made with drawing (vector) programs. Drawing, Scanning and Painting Pictures are "drawn" into vector graphics images using a digitizer tablet or mous. www.encyclopedia.com /html/v1/vector.asp   (467 words)

3. Differences between the Transactional and the Copenhagen Interpretations When applied to momentum space formalisms, etc, the issue of physical presence is moot, since it is not clear that ``physical presence'' in an arbitrary parameter space is a meaningful concept. Physical interactions with an observer are qualitatively different from other physical interactions because they produce observer knowledge and cause state vector collapse. Discussion: It was demonstrated in my review article[1] that at the interpretational level a paradox arises if one assumes (1) the CI account of state vector collapse and (2) that a single state vector describes a system involving two separated measurement events not lying in the same light cone. www-users.york.ac.uk /~mijp1/transaction/ti_over/node3.html   (910 words)

PH201 Chapter 1 Notes   (Site not responding. Last check: 2007-10-15) Vector addition can be accomplished graphically (head-to-tail method) or mathematically (resolution of vectors into components using trigonometry.) You are responsible for both techniques though the trigonometric solution is more important for work in physics. Either technique is appropriate for any and all types of vectors. Any vector can be arbitrarily resolved (divided) into any number of vectors, the sum of which equals the original. www.physics.orst.edu /~ketterj/COURSES/ph201/ch1.htm   (471 words)

Geometry: geometric objects and geometric database   (Site not responding. Last check: 2007-10-15) Nevertheless, all geometric objects have the need to encode (i) the mathematical representation(s) of the geometric object, (ii) the physical operations that exist for this object, as well as (iii) their symbolic properties. Other examples of physical operations are: finding the common perpendicular of two lines; inverting the direction of a velocity; generating the “exponential” curve generated by a given velocity; etc. This document uses the same names for the same physical operations in all spatial dimensions; by default, the 3D coordinate representations are given. www.orocos.org /documentation/geometry-doc.html   (3389 words)

[No title]   (Site not responding. Last check: 2007-10-15) The Vector interface supports both logical views of vectors via the view-specific methods, so the client can take whatever external view it wishes and thus does not really need to know the internal view used to implement the Vector abstration. Consequently, the external format or syntax of vectors on input streams is completely encapsulated in the Vector abstraction and hidden from the client - the client simply does not need to know this format. - Within a single instance of a "problem," Vector variables are used consistent with an object view; that is, variables always denote the same Vector instance - this is a virtue of the client code, not a virtue of the C language. longwood.cs.ucf.edu /~workman/cop4232/DesignStyles/OO1/vectorapp.cpp   (528 words)

Bibliographie des DLR (LIDO)   (Site not responding. Last check: 2007-10-15) Jacobian invariants of vector-field mappings onto physical space provide a topological characterization of flow structures and their changes in physical and in the vector-field spaces. On the other hand, the topological structures of flows (defined by any physical vector quantity of interest) are well-defined by singular flow surfaces in physical space. However, their geometric complexity in three-dimensional and/or unsteady flows suggests to monitor especially their local genesis occuring at higher-order degeneracies in physical space and/or singularities in spaces of components and/or invariants of vector-fields. www.dlr.de /lido/SM-SK/1999/1644241999.html   (212 words)

Relation of DWNs to FDNs is invariant with respect to insertion of a vector transformer (similarity transformation applied to the scattering matrix). In the case of physical waveguides of equal impedances, the eigenvector associated with the eigenvalue , we obtain (using a vector transformer) the larger class of scattering matrices which preserve an elliptic norm as induced by a positive-definite (or Hermitian) generalized junction impedance. ccrma-www.stanford.edu /~jos/cfdn/Relation_DWNs_FDNs.html   (654 words)

CalCoreSubmesh class Reference This function returns the vector that contains all physical properties of the core submesh instance. This function returns the vector that contains all texture coordinate vectors of the core submesh instance. This function sets the tangent vector associated with a specified texture coordinate pair in the core submesh instance. cal3d.sourceforge.net /docs/api/html/classCalCoreSubmesh.html   (753 words)

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