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Topic: Wedge product

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	Exterior algebra - Wikipedia, the free encyclopedia
		The wedge product is associative and bilinear; its essential property is that it is alternating on V:
		Any wedge product in which the same basis vector appears more than once is zero; any wedge product in which the basis vectors don't appear in the proper order can be reordered, changing the sign whenever two basis vectors change places.
		As in the case of tensor products of multilinear maps, the number of variables of their wedge product is the sum of the numbers of their variables.
	en.wikipedia.org /wiki/Wedge_product (1201 words)

	Wedge (disambiguation) - Wikipedia, the free encyclopedia
		In mathematics, the wedge product or the wedge sum.
		Among golf clubs, a wedge is a specialized type of iron.
		In U.S. geography, the Wedge is part of the border between Delaware and Pennsylvania.
	en.wikipedia.org /wiki/Wedge (197 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		In mathematics, the wedge product, also known as exterior product, is an anti-symmetrisation (alternation) of the tensor product.
		The wedge product is a distributive associative multiplication of skew-symmetric multilinear maps which is anti-commutative for maps with odd number of variables and commutative otherwise.
		The wedge product of two vector spaces may be identified with the subspace of their tensor product generated by the skew-symmetric tensors.
	www.informationgenius.com /encyclopedia/e/ex/exterior_power.html (576 words)

	PlanetMath: exterior algebra (Site not responding. Last check: 2007-11-06)
		The exterior product is anti-symmetric in the sense that for all
		-vector symbols, and the algebra product is defined by linearly extending the wedge product to all of
		The axiomatics of the exterior product are needed to define differential forms and therefore play an essential role in the theory of integration on manifolds.
	planetmath.org /encyclopedia/ExteriorAlgebra.html (449 words)

	Wedge Clamp Systems - History
		The Wedge Clamp System was invented in 1982 when a large production collision repair facility, in Vancouver, BC, Canada began to experiment with new repair production techniques to address changing industry requirements.
		The development of the Wedge Clamp System was based on field research, which confirmed that technicians preferred to avoid complicated systems – they wanted to work 'smarter' and not 'harder'.
		The basic design of the Wedge Clamp System represented an entirely new approach that was less expensive, easier to use, and would ensure repairs were made to original factory specification.
	www.wedgeclamp.com /history.htm (595 words)

	Area and Volume of Parallelograms and Parallelepipeds
		This is helpful because the geometric product of geometric products is simpler than the geometric product of wedge products.
		A more general way of taking the geometric product of two wedge products is to expand both wedge products in terms of geometric products according to equation 16, and then multiplying everything term-by-term.
		This can be handled by wedge products, as shown in figure 1 where the green bivector is the initial angular momentum, the small purple bivector is torque*time, and the yellow bivector is the new angular momentum, which is in a new orientation due to precession.
	www.av8n.com /physics/area-volume.htm (826 words)

	THE METTLER WEDGE (Product Review) (Site not responding. Last check: 2007-11-06)
		The product's website www.skyvalleyscopes.com/mettler.htm gave a good general description of the wedge, however, there were still a few concerns I had that were not covered.
		This is accomplished by placing the wedge on a hard surface (preferably the floor) and attaching the scope to the tilt plate.
		The wedge is then placed on top of the tripod, and the appropriate center-bolt hole (the one closest to the pre-determined balance point) is aligned over the tripod center-bolt.
	members.aol.com /planclos/index/mettler.htm (2643 words)

	GolfDigest.com - The Winning Wedge (Site not responding. Last check: 2007-11-06)
		This can get technical, but here's the bottom line: In general, wedges with a wide sole and a higher bounce angle are effective in lush fairways and soft sand, whereas wedges with a narrower sole and a lower bounce angle are better for firm, tightly mown fairways and firm sand.
		Be prepared for your specialty wedges to feel a bit heavier than the rest of the clubs in your bag.
		wedges have a classic teardrop shape and are cast from heat-treated, mild carbon steel.
	www.golfdigest.com /gfw/gfwequip/index.ssf?/gfw/gfwequip/gfw200304wedges.html (1441 words)

	CSDC : Cartan's Calculus: the interior product. (Site not responding. Last check: 2007-11-06)
		The interior product operation may look like the scalar product of ordinary vector analysis, but the idea is a bit more complex.
		Hence, the inner product of a p-form and a contravariant vector density pulled back is well defined in terms of the interior product of the pullback of the p-form and the pull back of the contravariant vector density.
		The interior product is often utilized in terms of a contravariant vectors, not contravariant vector densities, but then the result is only well defined with respect to diffeomorphisms, for which the inverse Jacobian is defined.
	www22.pair.com /csdc/ed3/ed3fre5.htm (460 words)

	[No title]
		Dot products, cross products, div, curl, grad, Gauss' Theorem, Stokes Theorem, the fundamental theorem of calculus --- all are primitive notions of vector spaces which have their origins in differential forms.
		Describe the wedge product of a one-form and a two-form.
		The first rule is that d is distributive over addition: d[w1_ + w2_] := d[w1] + d[w2] The second rule is a wedge product rule: d[w1^w2] = d[w1]^w2 +- w1^d[w2], where the sign is (-1) to the length of the forms w1.
	www.physics.cornell.edu /sethna/teaching/forms/forms.answers (1276 words)

	P-vector (Site not responding. Last check: 2007-11-06)
		A p-vector in differential geometry is the tensor obtained by taking linear combinations of the wedge product of p tangent vectors, for some integer p ≥ 1.
		A bivector is therefore an element of the antisymmetric tensor product of a tangent space with itself.
		In geometric algebra, also, a bivector is a grade 2 element (a 2-vector) resulting from the wedge product (see exterior algebra) of two vectors, and so it is geometrically an oriented area, in the same way a vector is an oriented line segment.
	www.worldhistory.com /wiki/P/P-vector.htm (325 words)

	Eidolon V-Sole Wedge - Eidolon
		Eidolon Wedges are precision cast of mild 8620 carbon steel.
		EIDOLON V-SOLE wedges are built on patented sole technology that allows the use of TWO bounce angles on each wedge.
		Pitching wedges have gotten stronger over the years and golfers have found themselves with a large distance void between their pitching and sand wedges.
	www.intheholegolf.com /thestore/prods/EVSW.html (669 words)

	Cartan's Calculus: the interior product. (Site not responding. Last check: 2007-11-06)
		None of the last two concepts, the concept of wedge exterior product, and the concept of the exterior derivative depend upon the notion of a metric space.
		However it is best to think of the interior product as an operation that linearly takes a p element into a p-1 element of the exterior algebra.
		The interior product is often utilized in terms of a contravariant vector, but then the result is only well defined with respect to diffeomorphisms.
	www.uh.edu /~rkiehn/ed3/ed3fre5.htm (271 words)

	Smithers Oasis Grower Products
		The product is a non-toxic thermoset phenolic resin, specifically engineered for an optimum balance of air and water resulting in faster root growth.
		This product is designed to drain off excess water from the base of the seed or cutting, while still providing proper balance of water and air for good root development.
		There is a light nutrient charge (1-1-1) in the Rootcube and Wedge products to supply it with nourishment until root initiation.
	www.smithersoasis.com /us/grower/faq.php (908 words)

	Tuning-Math Archive Section 3: 2100 - 2124
		Then the wedge product h^g = [u1,u2,u3,u4]^[v1,v2,v3,v4] is defined as: [u1[v2,v3,v4]-v1[u2,u3,u4], [u2,u3,u4] X [v2,v3,v4]] Written out in full, this is h^g = [u1v2-v1u2,u1v3-v1u3,u1v4-v1u4,u3v4-v3u4, u4v2-v4u2,u2v3-v2u3] Note that the first three elements of the wedge invariant, defined from any starting place, gives the mapping to primes of the non- octave generator of the pair of generators.
		The triple wedge product of three 7-limit intervals is the val we get by putting the three intervals in as rows of a 4x4 matrix and making the top row the four basis vectors.
		The wedge product of two intervals will be in a space of dimension n choose 2 = n(n-1)/2, and the length of the vector in the ordinary norm will be the area of the paralleogram defined by the two intervals, and the direction will be defined by the orientation of the paralleogram.
	www.robertinventor.com /tuning-math/s___3/msg_2100-2124.html (5523 words)

	Simpson Anchor Systems: WEDGE-ALL® (Site not responding. Last check: 2007-11-06)
		The Wedge-All is a non-bottom bearing, wedge style expansion anchor for use in solid concrete or grout filled masonry.
		Wedge anchors shall be a threaded stud with an integral cone expander and a single piece expansion clip.
		The stud shall be carbon steel with a minimum 70,000 psi tensile strength, or type 303, 304 or 316 stainless steel, as called for on the drawings.
	www.simpsonanchors.com /catalog/mechanical/wedge-all (272 words)

	Amazon.com: Baby: Safe Lift Deluxe Crib Wedge (Site not responding. Last check: 2007-11-06)
		The wedge is 26 inches wide (spanning the width of a standard crib mattress) and tapers over its 14-inch width to a maximum of 3 inches in thickness.
		When the wedge was under the mattress, he was constantly sliding down and/or repositioning himself in order to lay flat anyway.
		The wedge has a slight enough incline that she has proper drainage of her congestion, yet small enough that she does not slide down to the bottom of her crib.
	www.amazon.com /exec/obidos/tg/detail/-/B000056J6Q?v=glance (1337 words)

	Wedge (Site not responding. Last check: 2007-11-06)
		In mathematics, there is something called the wedge product in exterior algebra and the wedge sum in algebraic topology.
		But wedges are often talked about separately, placed in their own category, because they are specialized irons.
		The gap wedge, sand wedge and lob wedge are often sold separately, or as a 3-club subset.
	www.infothis.com /find/Wedge (606 words)

	Differential Forms and the Generalized Stokes Theorem
		The wedge product of two differential forms can be computed by creating their formal product and reducing it using the above relations.
		Although the definition of the derivative of the wedge product of 1-forms is as given above this is not the general formula for the derivative of the wedge product of differential forms of arbitrary degree.
		The same sign would apply to each wedge product of the product terms in the wedge product of a general i-form with a general j-form.
	www.sjsu.edu /faculty/watkins/difforms.htm (1932 words)

	Desk Wedge (4 Sizes) - BRONZE-DeskWedge
		This product is a custom bronze casting and ships in 3 to 4 weeks.
		Production time is NOT GUARANTEED and may run longer.
		You are allowed to print or email these images only in connection with the purchase of a product from us.
	www.plaxx.com /detail.aspx?ID=154 (295 words)

	Simpson Anchor Systems: FAQs (Site not responding. Last check: 2007-11-06)
		At this time the ET product was being manufactured by Ackerman-Johnson Fastening Systems of Addison, Illinois, a respected manufacturer who started the anchor industry in 1902.
		Since entering the anchor industry, the product line has been expanded to include 3 other adhesive anchor formulations, 2 crack injection epoxy formulations, a vinylester glass capsule anchor, a full line of mechanical anchors and carbide drill bits for masonry and concrete.
		A: Simpson Wedge-All wedge anchors have been tested under ICBO's AC01 Acceptance Criteria for Expansion Anchors in Concrete Masonry Elements and are listed to resist seismic loads in concrete with an allowable load increase of 33 -1/3%.
	www.simpsonanchors.com /technicalinfo/faqs.html (1445 words)

	Wedge (Site not responding. Last check: 2007-11-06)
		Technically a portable double inclined plane, a wedge is a simple machine used to separate two objects, or portions of objects, through the application of force, perpendicular to the inclined surfaces, developed by conversion of force applied to the blunt end.
		The mechanical advantage of a wedge depends on the ratio of it length to its thickness.
		In mathematics, there is something called the wedge product.
	www.sciencedaily.com /encyclopedia/wedge (167 words)

	Comparing Complex Numbers to Clifford Algebra (Site not responding. Last check: 2007-11-06)
		Other operations, including dot product and wedge product, will be defined in terms of the geometric product.
		Quite generally, we define the dot product as follows: The dot product of a scalar with anything is zero.
		Otherwise, the dot product of two multivectors is the low-grade piece of the geometric product.
	www.av8n.com /physics/complex-clifford.htm (1128 words)

	Articles - Cross product (Site not responding. Last check: 2007-11-06)
		The cross product of the two vectors a and b is denoted by a × b (in longhand some mathematicians write a∧b to avoid confusion with the letter x).
		Which vector is the "correct" one by convention depends upon the orientation of the vector space—i.e., on the handedness of the given orthogonal coordinate system (i, j, k).
		The vector cross product is an example of a non-associative map.
	www.gaple.com /articles/Cross_product (1085 words)

	Differential Forms: Algebra of Forms
		Also, the wedge product is antisymmetric wrt the arguments of the functionals: (f^g)[x,y] = - (f^g)[y,x].
		Here, we see that the wedge product is symmetric instead of being antisymmetric if one of the arguments is a 2-form: F^h = h^F if F is a 2-form and h a 1-form.This can be easily deduced from elementary properties of the wedge products including linearity, associativity and antisymmetry when acting on 1-forms:
		In general, the wedge product of a k-form and an m-form gives a (k+m)-form, ie, a linear functional on R^(k+m).
	www.physics.cornell.edu /sethna/teaching/forms/forms_2_0_0.html (1448 words)

	wedge.html
		Procedure 'wedge' defines an exterior (wedge) product of any number of Clifford polynomials p1, p2,..., pn.
		Via the procedure 'rmulm', wedge multiplication may be applied to matrices with entries in a Clifford algebra or in an exterior algebra.
		Error, (in wedge) argument(s) contain(s) index larger then current value of dim_V which is now, 2, To complete computation, increase value of dim_V or assign square matrix of size at least, 4, by, 4, to bilinear form B
	math.tntech.edu /rafal/cliff5/Samples/wedge1.html (659 words)

	Western Forms (Site not responding. Last check: 2007-11-06)
		From simple, yet tough pin & wedge, bracket, and clip designs to the industry's best attached hardware in the PinLock system, the pieces bringing your forms together meet the same high standards as the premier Western Forms forming systems.
		Inexpensive disposable capping clip for those who prefer to use a wedge to secure the capping clip to the form.
		The ratchet action allows you to insert the wedge to various depths in the pin slot, all the way to full insertion.
	www.westernforms.com /products.aspx?id=13 (367 words)

	Clifford Algebra
		Note that the parallelogram itself is the wedge product:not the area (that equals the magnitude V
		The symmetric part of the geometric product is the dot product; the antisymmetric part is the wedge product.
		From the symmetry properties of the geometric product we calculate the square of the unit trivector
	home.pcisys.net /~bestwork.1/Clifford/clifford.htm (514 words)

	Company News On Call (Site not responding. Last check: 2007-11-06)
		The new product lines will be introduced at the Professional Golf Association (PGA) Show to be held in January 2001 in Orlando, Florida.
		Our companies are committed to providing leading edge golf products that enhance performance and deliver consistency." Robert J. Bettinardi, president of Bettinardi Golf, commented, "We are excited to team with Royal Precision in combining our technologies to deliver innovative, performance enhancing products.
		The synergy created between our companies has led to dynamic new product lines designed to provide golfers of all playing ability the opportunity to optimize their game.
	www.prnewswire.com /cgi-bin/stories.pl?ACCT=105&STORY=/www/story/12-11-2000/0001383518 (596 words)

	Demco Offers Preferred Integrator Program
		Demco Wedge products are modular, scalable, re-usable and reconfigurable
		the Demco Wedge Base Chassis is designed with the lean philosophies of flexibility, technician-friendly operation and ergonomics, ease of reconfiguration to handle product changes and new products, and operator interface at the station level to keep equipment running in the event of breakdown or line trouble.
		Choose your base Wedge chassis starting as low as $44,500 (rotary dial, in-line or walking beam) with built-in power, electrical, air, and controls distribution.
	www.demcowedge.com /dw_integrators.html (370 words)

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