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Topic: Scalar product

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	PlanetMath: triple scalar product
		The triple scalar product of three vectors is an extension of the cross product.
		Thus, the magnitude of the triple scalar product is equivalent to the volume of the parallelepiped formed by the three vectors.
		The latter is implied by the properties of the cross product.
	planetmath.org /encyclopedia/TripleScalarProduct.html (238 words)

	Scalar Product of Vectors
		The scalar product and the vector product are the two ways of multiplying vectors which see the most application in physics and astronomy.
		The vectors A and B cannot be unambiguously calculated from the scalar product and the angle.
		The scalar product is used for the expression of magnetic potential energy and the potential of an electric dipole.
	hyperphysics.phy-astr.gsu.edu /hbase/vsca.html (266 words)

	A (Site not responding. Last check: 2007-10-08)
		the vector product of pseudo-vectors is a pseudo-vector.
		the vector product of a pseudo-tensor and a psuedo-vector is a pseudo-tensor.
		inverse of a vector is defined by analogy to the inverse of a scalar: the scalar
	www.cchem.berkeley.edu /jsngrp/Che250/HW1.htm (958 words)

	Calculation of a scalar product in a direct-type FIR filter - Patent 6131105
		The method for calculating a scalar product of claim 1 wherein bit serial multiplying is accomplished by delaying each of the partial scalar products by a selected delay period to shift said scalar product to perform a multiplication by a power of two.
		The scalar product calculator of claim 7 wherein each of the multiplication elements is comprising a plurality of delaying elements to delay each of the partial scalar products by a selected delay period to shift said scalar product to perform a multiplication by a power of two.
		The scalar product calculator of claim 7 wherein the summing element is comprising a plurality of adder/subtractor elements placed at the output of multiplication elements to accumulate the plurality of partial scalar products.
	www.freepatentsonline.com /6131105.html (4301 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Both products can be computed algebraically in terms of the components of the vectors, and geometrically in terms of the magnitudes and directions of the vectors.
		The vector product can be used to test whether two vectors are parallel, to compute the area of a parallelogram determined by two vectors and to find vectors in 3-space that are orthogonal to two given vectors.
		Formulas: Formulas for the dot and cross products, both algebraic (in terms of the components of the vectors) and geometric (in terms of the magnitudes of the vectors and the angle between the vectors); formulae for 2x2 and 3x3 determinants (needed to compute cross products); basic properties of the dot product (p.
	www.math.uiuc.edu /~dikim/m242/lec2.html (980 words)

	PlanetMath: dyad product
		Likewise, the scalar factor transfer rule is valid.
		and the product of such dyads as (1) to be the formal sum of individual products (3).
		This is version 11 of dyad product, born on 2005-08-04, modified 2005-08-31.
	planetmath.org /encyclopedia/DyadProduct.html (239 words)

	Dot product -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Thus the scalar value of the fraction must be less than or equal to 1 and can be easily translated into a angular value (As the trigonometric functions are really nothing more than Taylor approximated functions to achieve a seamless translation table of lengths into angle values and vice versa (arcsin,...).
		The dot product is particularly used in the calculation of (Click link for more info and facts about net force) net force.
		The dot product satisfies all the axioms of an (A real number (a scalar) that is the product of two vectors) inner product.
	www.absoluteastronomy.com /encyclopedia/d/do/dot_product.htm (977 words)

	MSN Encarta - Search Results - scalar product
		For example, 8 is the product of 2 × 4 and 30 is the product of 5 * 6.
		Product Safety, issues surrounding the design and manufacture of consumer products that do not present undue hazards to their users.
		Product Safety, advertising, marketing, and merchandising, compared with services, consumer testing, distribution, high failure rate of new...
	encarta.msn.com /scalar%2bproduct.html (147 words)

	Help for the ScalarProduct package for Maple (Site not responding. Last check: 2007-10-08)
		scalar determines a system of differential equations satisfied by , the scalar product (of symmetric functions) of F and G. Symbolic scalar products can be calculated by using the variables 'pn' where n is any symbol.
		This is equivalent to the scalar product .
		This product arises in the study of the tensor product of characters of representations of the symmetric group.
	www.labri.u-bordeaux.fr /Perso/~mishna/SP/SP.html (660 words)

	Page 433 (Site not responding. Last check: 2007-10-08)
		As the name says, a scalar product of two vectors results in a scalar quantity, and a vector product in a vector quantity.
		The result of this product is a scalar quantity.
		The scalar product between two vector is denoted by a thick dot:
	lectureonline.cl.msu.edu /~mmp/kap17/cd433.htm (125 words)

	Products Involving Vectors
		The product of a scalar and a vector is another vector with the same direction as the original vector, but with a different magnitude.
		Given two vectors, their scalar product is defined as the product of their magnitudes times the cosine of the angle between them.
		The magnitude fo the vector product is equivalent to the area of teh parallelogram determined by teh two vectors multiplied.
	www.geocities.com /EnchantedForest/5600/vector2.html (466 words)

	Method and a circuit for encoding a digital signal to determine the scalar product of two vectors, and corresponding ...
		The value of the scalar product of the vectors mentioned above is expressed in accordance with the present invention by a scalar product value function written: ##EQU6## and the method of the invention, as shown in FIG.
		It will naturally be understood that the two scalar product evaluation functions correspond, in fact, to taking account of two subsets of coefficients from the first row of above-described matrix A or B in association with the values of the combined variable components x0 to x7, for example.
		Each product of a subvector and the variable components corresponding to the results y0, y2, y4 & y6 and y1, y3, y5 & y7 respectively is obtained via a summing circuit 3 such as that shown in part a or b of FIG.
	www.freepatentsonline.com /5218565.html (5741 words)

	Scalar Product (Site not responding. Last check: 2007-10-08)
		A real number (a scalar) that is the product of two vectors.
		= AB cos?If a scalar product is zero, one of the vectors is zero or else the two are perpendicular.
		English words defined with "scalar product": dot product ♦ inner product.
	www.websters-online-dictionary.org /sc/scalar+product.html (332 words)

	Vector Operations
		Scalar Product: The simplest way to multiply two vectors is called the scalar product (often called the dot product).
		We usually use the scalar product when what is important is not the whole magnitude of a vector, but only its magnitude along some direction.
		There are several ways to compute the vector product, but the most useful way for this course is to memorize the rules for the cross products of the unit vectors.
	maxwell.byu.edu /~spencerr/websumm122/node8.html (738 words)

	Scalar (Site not responding. Last check: 2007-10-08)
		This is the scalar product of the two vectors F and a and can be seen as a geometric definition.
		The scalar product is a product of vectors
		Use of the "dot" is essential to indicate that the calculation is a scalar product.
	www.efm.leeds.ac.uk /CIVE/CIVE1630/Notes/scalar.html (182 words)

	PlanetMath: invariant scalar product
		is by definition an invariant scalar product as above where the representation is the adjoint representation of
		Thus an invariant scalar product (with respect to a Lie algebra representation) is sometimes called an associative scalar product.
		This is version 3 of invariant scalar product, born on 2005-09-09, modified 2005-09-21.
	planetmath.org /encyclopedia/InvariantScalarProduct.html (245 words)

	Vector : Scalar product (Site not responding. Last check: 2007-10-08)
		The dot product of two vectors a and b (also called the inner product, or, since its result is a scalar, the scalar product) is denoted by a·b or sometimes by (a, b) and is defined as:
		The cross product (also vector product or outer product) differs from the dot product primarily in that the result of a cross product of two vectors is a vector.
		Because the cross product depends on the choice of coordinate systems, its result is referred to as a pseudovector.
	www.eurofreehost.com /sc/Scalar_product_5.html (508 words)

	Vector : Scalar product (Site not responding. Last check: 2007-10-08)
		First, the absolute value of the box product is the volume of the parallelepiped which has edges that are defined by the three vectors.
		Second, the scalar triple product is zero if and only if the three vectors are linearly dependent, which can be easily proved by considering that in order for the three vectors to not make a volume, they must all lie in the same plane.
		In coordinates, if the three vectors are thought of as rows, the scalar triple product is simply the determinant of the 3-by-3 matrix having the three vectors as rows.
	www.eurofreehost.com /sc/Scalar_product_6.html (325 words)

	Dot Product (Site not responding. Last check: 2007-10-08)
		This java applet demonstrates the dot product, which is an important concept in linear algebra and physics.
		The projection of A onto B is shown in yellow, and the angle between the two is shown in orange.
		At the bottom of the screen are four bars which show the magnitude of four quantities: the length of A (red), the length of B (blue), the length of the projection of A onto B (yellow), and the dot product of A and B (green).
	www.falstad.com /dotproduct (163 words)

	Vectors: Scalar Product (Site not responding. Last check: 2007-10-08)
		product is a way of multipling two vectors to produce a
		Using the dot products between the unit vectors, the dot product between A and B - which has nine dot products between the unit vectors, out of which six are zero is arrived at by
		The useful dot products are between the same unit vectors
	www.rit.edu /~pnveme/pigf/Vectors/vector_dot_1.html (85 words)

	PHY 206 Review of Dot Product / Dr. Miner (Site not responding. Last check: 2007-10-08)
		It is to use the Scalar Product, or the Dot Product.
		Thus the result of Dot Product, or Scalar Product is simply a scalar.
		This simplifies the process since we note that the dot product of a unit vector with itself is equal to (1)(1)cos(0) = "1," whereas the dot product of two different unit vectors is always zero.
	www.udayton.edu /~physics/gkm/rdot.htm (247 words)

	Vector Space
		The scalar product is defined for two vector operands with the result being a scalar.
		Therefore, the scalar product too is not a group operation.
		The scalar product of two vectors a and b is denoted a.
	www.cut-the-knot.com /do_you_know/mul_scal1.shtml (310 words)

	Scalar Product (Site not responding. Last check: 2007-10-08)
		He then produces a definition of the scalar product of 2 general vectors in terms of the square of the magnitude of the base vector and the scalar multiple.
		Up to the introduction of the scalar product the vector algebra tools available to deal with geometry do not allow for any handling of angles.
		Once the scalar product has been defined then angles can be measured and manipulated.
	s13a.math.aca.mmu.ac.uk /Geometry/Vectors/ScalarProd/ScalarProduct.html (255 words)

	Scalar Product (Site not responding. Last check: 2007-10-08)
		The other number is the length of the other vector, a scalar, times the cosine of the angle between them, a scalar, so our second factor, being the product of two scalars is a scalar.
		The scalar nature of the dot product can be confirmed by carrying out the term by term multiplication of the two vectors, just as though they were polynomials, including in each term the unit vector which gives the component its direction.
		The dot product of a unit vector with itself is 1.
	www.mcasco.com /qa_vsp.html (240 words)

	Module 4: Further vectors - Section 2
		The scalar triple product of the three vectors a, b and c is the scalar
		One use of the scalar triple product is to establish whether three vectors lie in the same plane, that is, are coplanar.
		Recall that the cross product of two vectors is a vector that is at right-angles to both the original vectors.
	www.es.ucl.ac.uk /undergrad/geomaths/4-vec/vec2.htm (267 words)

	amychris:Desktop Folder:MHvecslnk8.html
		In fact the scalar product is so-called because the result of the multiplication is a scalar.
		The scalar product of a and b is denoted a.b (hence the other name for it: the "dot product").
		Now we use our results that the dot product of a unit vector with another unit vector is zero, and that the dot product of a unit vector with itself is 1, to simplify these nine terms.
	www.ucl.ac.uk /Mathematics/geomath/vecsnb/MHvecslnk8.html (908 words)

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