Scalar (mathematics)

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Topic: Scalar (mathematics)

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	VecProd.doc
		In mathematics the word scalar is used for a dimensionless number, like 6, as opposed to a vector.
		The triple scalar product of vectors A, B, and C is given by A.(BxC) and the volume of a tetrahedron is 1/6 this value.
		If we extract this number we get a pure scalar number which is the dot product.
	www.pballew.net /VecProd.doc (1907 words)

	UC Berkeley Mathematics
		Stochastic estimates of basic ﬂuxes arising from a ﬁnite-volume representation of the Navier-Stokes equations and the equation for a passive scalar undergoing turbulent mixing require multi-point correlations of velocities and scalars as inputs.
		It is shown that there exists an ideal LES model for turbulent mixing which preserves all singletime, multi-point velocity-scalar joint statistics.
		These correlations are obtained using Kolmogorov's inertial range theory and Obukhov's theory for passive scalar transport.
	math.berkeley.edu /calendar-event567.html (317 words)

	Scalar - Wikipedia, the free encyclopedia
		In mathematics, physics, and computing, a scalar is a quantity usually characterized by a single numeric value or not involving the concept of direction.
		In mathematics, scalars are components of vector spaces (and modules), usually real numbers which can be multiplied into vectors by scalar multiplication, or produced from vectors by scalar product.
		In physics, a scalar is a simple physical quantity that does not change under a change of coordinate system; for example, speed (180 km/h) is a scalar, while velocity (180 km/h north) is a vector.
	en.wikipedia.org /wiki/Scalar (265 words)

	Scalar potential: Facts and details from Encyclopedia Topic
		In mathematics and physics, a scalar field associates a single number (or scalar) to every point in space....
		In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a euclidean space....
		In vector calculus a solenoidal vector field is a vector field v with divergence zero:...
	www.absoluteastronomy.com /encyclopedia/s/sc/scalar_potential.htm (1553 words)

	commutative law -- Encyclopædia Britannica
		in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba; that is, a finite sum or product is unaltered by reordering the terms or factors.
		in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + (b + c) = (a + b) + c, and a(bc) = (ab)c; that is, the terms or factors may be associated in any way desired.
		A ring satisfying the commutative law of multiplication (axiom 8) is known as a commutative ring.
	www.britannica.com /eb/article-9024995 (900 words)

	[Mind Control Research Forum] scalar link
		In mathematics, when you say something is a scalar, you're just speaking of a number, without having a direction attached to it.
		Of course, if the standing scalar potential wave is a sine wave function of the radial distance from the source, and the Geiger counter is at the node, it will not read because there is no difference there from normal ambient vacuum potential.
		Summing that up, physically a scalar thing is a thing that (1) is a vector in time, which is hidden from direct observation, (2) externally is just a magnitude spatially, and (3) has an internal spatial vector structure, and therefore a hyperspatial or virtual-state vector structure.
	www.tinyurl.com /8ebhq (12451 words)

	Earliest Known Uses of Some of the Words of Mathematics (V)
		Vector and scalar also appear in 1846 in a paper "On Symbolical Geometry," in the The Cambridge and Dublin Mathematical Journal vol.
		The first occurrence of vector and scalar in the London, Edinburgh, and Dublin Philosophical Magazine is in volume XXIX (1846) in the article "On Quaternions; or on a new System of Imaginaries in Algebra":
		The story begins with a technical term in theoretical astronomy, "radius vector," in which "vector" signified "carrier." In the first and biggest change "radius" was dropped and "vector" was given a place in the algebra of quaternions (c.
	members.aol.com /jeff570/v.html (12451 words)

	Vector Spaces
		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.
		In proving theorems we can use axioms, previous theorems, and facts from earlier mathematics courses.
		, what is the result of multiplying a vector by the scalar
	distance-ed.math.tamu.edu /Math640/chapter3/node4.html (12451 words)

	Characteristic equation
		In mathematics, in the field of linear algebra, a scalar $\Phi$ is an eigenvalue of an n-by-n matrix if $\Phi$ satisfies the Characteristic Equation: $det(A-\Phi I_n) = 0$ whereIn is the Identity matrix.
		In mathematics, in the field of linear algebra, a scalar $\Phi$ is an eigenvalue of an n-by-n matrix if $\Phi$ satisfies the Characteristic Equation:
		The way is open in the Congress of say that values are restored and that the Congress will, therefore, repeal because national income has grown with rising prosperity, we shall repeal and of starting to reduce the national debt?
	www.termsdefined.net /ch/characteristic-equation.html (12451 words)

	Math::Vector - package containing functions for vector mathematics and associated operations
		Returns a vector which is the result of multiplying a vector by a mathematical scalar.
		Note that the first value passed to the method is the mathematical scalar quantity by which the vector is multiplied.
		People using this module are assumed to know basic vector mathematics and trigonometry, so the theory behind the methods will not be explained.
	cpan.uwinnipeg.ca /htdocs/Math-Vector/Math/Vector.html (12451 words)

	Review of vector Mathematics
		In dynamics the dot product is used to define work and power, to reduce a vector to components, and to reduce vector equations to scalar equations.
		is a vector, the cross product is also called the vector product to distinguish it from the scalar product (the dot product).
		The first distributive law above may be used (in lieu of the determinant formula) to compute cross products in terms of the cartesian components of the vectors.
	www.eng.fsu.edu /~ecollins/dynamics/vectors (12451 words)

	The Quest Part 3
		A six-foot tall scalar triangular radiating membrane, which is slightly curved at the base, would be ideal.
		But the laws of physics and mathematics regarding slots is resolute and cannot be broken or altered.
		These are one, a vertical slot at least 6 feet long and preferably 7 fThe second is a scalar triangular diaphragm with the top aperture at least 6 feet off the floor.
	www.ampzilla2000.com /thequest3.html (12451 words)

	Scalar multiplication - Wikipedia, the free encyclopedia
		In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
		Scalar multiplication may be viewed as an external binary operation or as an action of the field on the vector space.
		A geometric interpretation to scalar multiplication is a stretching or shrinking of a vector.
	en.wikipedia.org /wiki/Scalar_multiplication (334 words)

	Scalar - Wikipedia, the free encyclopedia
		In mathematics, the meaning of scalar depends on the context; it can refer to real numbers or complex numbers or rational numbers, or to members of some other specified field.
		In physics, a scalar is a physical quantity which assumes a single value which is independent of the coordinate system being used to describe the physical system.
		The components of a vector as such are not scalars, since they change with a change of coordinate system; a scalar field may however for one choice of the coordinate system be equal to a particular component.
	en.wikipedia.org /wiki/Scalar (861 words)

	Scalar multiplication - Wikipedia, the free encyclopedia
		In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
		Scalar multiplication may be viewed as an external binary operation or as an action of the field on the vector space.
		A geometric interpretation to scalar multiplication is a stretching or shrinking of a vector.
	www.wikipedia.org /wiki/Scalar_multiplication (332 words)

	Scalar field - Wikipedia, the free encyclopedia
		For the field of scalars of a vector space, see scalar (mathematics).
		In scalar theories of gravitation scalar fields are used to describe the gravitational field.
		Scalar fields are found within superstring theories as dilaton fields, breaking the conformal lsymmetry of the string, though balancing the quantum anomalies of this tensor
	www.wikipedia.org /wiki/Scalar_field (546 words)

	Vector space - Wikipedia, the free encyclopedia
		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.
		A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra.
		It is this abstract quality that makes it useful in many areas of modern mathematics.
	en.wikipedia.org /wiki/Vector_space (546 words)

	Magnitude - Wikipedia, the free encyclopedia
		In physics, the magnitude of a vector is a scalar in the physical sense, i.e.
		In mathematics, the magnitude of an object is a non-negative real number associated with that object.
		In seismology, the magnitude is a logarithmic measure of the energy released during an earthquake.
	en.wikipedia.org /wiki/Magnitude (184 words)

	Vector field - Wikipedia, the free encyclopedia
		In particular a vector field is not a bunch of scalar fields.
		Suppose we have a scalar field which is given by the constant function 1, and a vector field which attaches a vector in the r-direction with length 1 to each point.
		In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space.
	en.wikipedia.org /wiki/Vector_field (1398 words)

	Similarity (mathematics) - Wikipedia, the free encyclopedia
		A concept commonly taught in high school mathematics is that of proving the angle and side theorems, which can be used to define two triangles as similar (or indeed, congruent).
		One of the meanings of the terms similarity and similarity transformation (also called dilation) of a Euclidean space is a function f from the space into itself that multiplies all distances by the same positive scalar r, so that for any two points x and y we have
		Similarity of matrices does not depend on the base field: if L is a field containing K as a subfield, and A and B are two matrices over K, then A and B are similar as matrices over K if and only if they are similar as matrices over L.
	en.wikipedia.org /wiki/Similarity_(mathematics) (1162 words)

	Incidence matrix -- Facts, Info, and Encyclopedia article
		where is the adjacency matrix of the line graph of, is incidence matrix, and is the (A scalar matrix in which all of the diagonal elements are unity) identity matrix of dimension q.
		In this case the incidence matrix is also a (additional info and facts about biadjacency matrix) biadjacency matrix of the (additional info and facts about Levi graph) Levi graph of the structure.
		The incidence matrix is related to the (additional info and facts about adjacency matrix) adjacency matrix of its line graphgraph by the following theorem:
	www.absoluteastronomy.com /encyclopedia/i/in/incidence_matrix.htm (129 words)

	Coordinate system - Wikipedia, the free encyclopedia
		In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space.
		See Cartesian coordinate system or Coordinates (mathematics) for a more elementary introduction to this topic.
		In this sense coordinates are not scalars (although, of course, a scalar field can be defined which for one particular coordinate system corresponds to a particular coordinate).
	en.wikipedia.org /wiki/Coordinates (1163 words)

	Talk:Determinant - Wikipedia, the free encyclopedia
		Since the cross product can be defined as a determinant where the first row is comprised of unit vectors, it is easy to prove that the scalar triple product is the determinant of a matrix where each row is a vector.
		The determinant function is defined in terms of vector spaces.
		the determinant is the first sum subtract the second one.
	en.wikipedia.org /wiki/Talk:Determinant (937 words)

	Kids.net.au - Encyclopedia Vector -
		Vectors can be contrasted with scalar quantities such as distance, speed, energy, time, temperature, charge, power, work, and mass, which have magnitude, but no direction (they are invariant under coordinate rotations).
		This article is about the concept of vector in mathematics.
		In differential geometry, physics, and engineering, the term vector usually refers quantities that are closely related to the coordinates from Euclidean space (or to tangent spaces of a differentiable manifold)—the notion of having a "magnitude" and "direction" is formalized by saying that the vector has components that transform like the coordinates under rotations.
	www.kids.net.au /encyclopedia-wiki/ve/Vector (937 words)

	Mathematics
		Mathematics 3 and 8 cover the basic calculus of functions of a single variable, as well as vector geometry and calculus of scalar-valued functions of several variables.
		Prerequisite: Mathematics 8, or Mathematics 3 and 6.
		The mathematical methods of Mathematics 6, or Mathematics 20, and Mathematics 13 are extended and applied to the study of mathematical models developed for use in such fields as anthropology, biology, economics, sociology, psychology, and linguistics.
	www.dartmouth.edu /~reg/courses/desc/math.html (937 words)

	Mathematics
		Mathematics 3 and 8 cover the basic calculus of functions of a single variable, as well as vector geometry and calculus of scalar-valued functions of several variables.
		Prerequisite: Mathematics 8, or Mathematics 3 and 6.
		The mathematical methods of Mathematics 6, or Mathematics 20, and Mathematics 13 are extended and applied to the study of mathematical models developed for use in such fields as anthropology, biology, economics, sociology, psychology, and linguistics.
	www.dartmouth.edu /~reg/courses/desc/math.html (937 words)

	Mathematics
		Mathematics 3 and 8 cover the basic calculus of functions of a single variable, as well as vector geometry and calculus of scalar-valued functions of several variables.
		Prerequisite: Mathematics 8, or Mathematics 3 and 6.
		The mathematical methods of Mathematics 6, or Mathematics 20, and Mathematics 13 are extended and applied to the study of mathematical models developed for use in such fields as anthropology, biology, economics, sociology, psychology, and linguistics.
	www.dartmouth.edu /~reg/courses/desc/math.html (7640 words)

	ipedia.com: Scalar curvature Article
		In mathematics, the scalar curvature of a surface is the familiar Gaussian curvature.
		For higher-dimensional manifolds, it is double of the sum of all the sectional curvatures along all the 2-planes spanned by some orthonormal frame.
		It is also the full trace of the Ricci curvature as well as of the curvature tensor.
	www.ipedia.com /scalar_curvature.html (121 words)

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Topic: Scalar (mathematics)

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