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On Thursday, October 14, 2010 09:11:50 am James Holton wrote: > As I sit here listening to the giant "whoosh" sound of all the world's > biologists unsubscribing from the CCP4BB, I wonder if anyone on this > thread can explain to me the difference between a matrix and a tensor? In invoking the latter, one risks that Tension, apprehension, And dissension have begun. (and now that "whoosh" may encompass all our younger readers, biologists or not). As to electric current, note that its generalized description may include a vector corresponding to the spin state of the electrons that carry it. Relevant to electromagnets, if nothing else. Ethan > I ask because I think stress and strain are mechanisms of radiation > damage, but where I am stuck is that Young's modulus seems to always be > represented by a "tensor" (as opposed to something that makes sense). > This is not helped by the lack of a tensor class in stdlib! Isn't that just because real life materials and real life objects are easier to bend in in some directions than in other directions? > > However, I do think it is interesting that this same Thomas Young > performed a famous experiment in 1801 that (eventually) proved a single > photon can scatter off of two slits at the same time. This is one of > two experiments that can only be explained by quantum mechanics. > > -James Holton > stressed and strained scientist > > On 10/14/2010 8:22 AM, Ed Pozharski wrote: > > Again, definitions are a matter of choice. Under your strict version I > > still may consider electric current as vector, if I introduce the > > coordinate system in the circuit. When I transform the coordinate > > system (from clockwise to counterclockwise), current changes direction > > with it. By the way, check the *current density* - it is a vector and > > it obeys, in generalized case of an inhomogeneous material, a tensor > > form of Ohm's law. > > > > There is no "correct" definition of anything. Ian is right in the > > narrow sense of the conventional vector in multiple dimensions and, > > especially, regarding the software implementation. But there is a > > legitimate (i.e. not self-contradictory) broader definition of a vector > > as an element of vector space, and complex numbers fall under it. Math > > is flexible, and there is definite benefit of consider complex numbers > > (and electric current under some circumstances) as vectors. > > > > Checking out of semantics hotel, > > > > Ed. > > > > On Thu, 2010-10-14 at 16:47 +0200, Ganesh Natrajan wrote: > >> The definition of a vector as being something that has 'magnitude' and > >> 'direction' is actually incorrect. If that were to be the case, a > >> quantity like electric current would be a vector and not a scalar. > >> Electric current is a scalar. > >> > >> A vector is something that transforms like the coordinate system, while > >> a scalar does not. In other words, if you were to transform the > >> coordinate system by a certain operator, a vector quantity in the old > >> coordinate system can be transformed into the new one by using exactly > >> the same operator. This is the correct definition of a vector. > >> > >> G. > >> > >> > >> > >> On Thu, 14 Oct 2010 10:22:59 -0400, Ed Pozharski > >> <[log in to unmask]> wrote: > >>> The definition game is on! :) > >>> > >>> Vectors are supposed to have direction and amplitude, unlike scalars. > >>> Curiously, one can take a position that real numbers are vectors too, if > >>> you consider negative and positive numbers having opposite directions > >>> (and thus subtraction is simply a case of addition of a negative > >>> number). And of course, both scalars and vectors are simply tensors, of > >>> zeroth and first order :) > >>> > >>> Guess my point is that definitions are a matter of choice in math and if > >>> vector is defined as an array which must obey addition and scaling rules > >>> (but there is no fixed multiplication rule - regular 3D vectors have > >>> more than one possible product), then complex numbers are vectors. In a > >>> narrow sense of a real space vectors (the arrow thingy) they are not. > >>> Thus, complex number is a Vector, but not the vector (futile attempt at > >>> using articles by someone organically suffering from article dyslexia). > >>> > >>> Cheers, > >>> > >>> Ed. > >>> > >>> > >>> O > -- Ethan A Merritt Biomolecular Structure Center, K-428 Health Sciences Bldg University of Washington, Seattle 98195-7742