The proof of mass vector.
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From: mmeron on 4 Jul 2006 23:34 In article <050720060114040611%phineaspuddleduck(a)googlemail.com_NOSPAM>, Phineas T Puddleduck <phineaspuddleduck(a)googlemail.com_NOSPAM> writes: >In article <1152058227.247299.229410(a)a14g2000cwb.googlegroups.com>, >Ka-In Yen <yenkain(a)yahoo.com.tw> wrote: > >> Stupid physicists have been doing vector by vector division >> for a hundred years. They need a remedial course in vector >> algebra, not me. >> >> > A linear mass density is a scalar. >> >> That's not 3D vector algebra. > >http://mathworld.wolfram.com/VectorDivision.html > >There is no unique solution A to the matrix equation y=Ax unless x is >parallel to y, in which case A is a scalar. Therefore, vector division >is not defined. > I wouldn't quite say so. The proper terminology would be "not uniquely defined". Which, per se, is not a problem as long as the limitations are understood. We can (and do, under various occasions) use "pseudoinverses" in linear algebra. These occur when using singular matrices. While, of course, for a singular matrix A the inverse A^(-1) doesn't exist, one can define pseudoinverse of A a matrix A^(~1) such that for every vector fully in the "non null" subspace corresponding to A you've A^(~1)*Av = v. such a pseudoinverse exists though, again, it is not unique. No problem. In fact one can view the commonly used Green's functions as just such pseudoinverses. So, in a similar sense, division by a vector can be defined, though it is not unique. And uniqueness can be provided by adding an additional condition, for example taking as the multiplicative inverse of v the shortest of all vectors such that v /dot v^(-1) = 1. Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: Phineas T Puddleduck on 5 Jul 2006 08:47 In article <7rGqg.6$45.504(a)news.uchicago.edu>, <mmeron(a)cars3.uchicago.edu> wrote: > In article <050720060114040611%phineaspuddleduck(a)googlemail.com_NOSPAM>, > Phineas T Puddleduck <phineaspuddleduck(a)googlemail.com_NOSPAM> writes: > >In article <1152058227.247299.229410(a)a14g2000cwb.googlegroups.com>, > >Ka-In Yen <yenkain(a)yahoo.com.tw> wrote: > > > >> Stupid physicists have been doing vector by vector division > >> for a hundred years. They need a remedial course in vector > >> algebra, not me. > >> > >> > A linear mass density is a scalar. > >> > >> That's not 3D vector algebra. > > > >http://mathworld.wolfram.com/VectorDivision.html > > > >There is no unique solution A to the matrix equation y=Ax unless x is > >parallel to y, in which case A is a scalar. Therefore, vector division > >is not defined. > > > I wouldn't quite say so. The proper terminology would be "not > uniquely defined". Which, per se, is not a problem as long as the > limitations are understood. > > We can (and do, under various occasions) use "pseudoinverses" in > linear algebra. These occur when using singular matrices. While, of > course, for a singular matrix A the inverse A^(-1) doesn't exist, one > can define pseudoinverse of A a matrix A^(~1) such that for every > vector fully in the "non null" subspace corresponding to A you've > A^(~1)*Av = v. such a pseudoinverse exists though, again, it is not > unique. No problem. In fact one can view the commonly used Green's > functions as just such pseudoinverses. > > So, in a similar sense, division by a vector can be defined, though it > is not unique. And uniqueness can be provided by adding an additional > condition, for example taking as the multiplicative inverse of v the > shortest of all vectors such that v /dot v^(-1) = 1. > > Mati Meron | "When you argue with a fool, > meron(a)cars.uchicago.edu | chances are he is doing just the same" Yep the latter bit did add the disclaimer "not uniquely" but I thought it was worth pushing his way ;-) -- Relf's Law? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ "Bullshit repeated to the limit of infinity asymptotically approaches the odour of roses." -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ Jaffa cakes. Sweet delicious orangey jaffa goodness, and an abject lesson why parroting information from the web will not teach you cosmology. -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ Official emperor of sci.physics, head mumbler of the "Cult of INSANE SCIENCE". Please pay no attention to my butt poking forward, it is expanding. -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ PWNER of Vert and TomGee since 2006 "I don't know that much math." - tomgee; 2 April 2006 "I don't claim to know what I'm talking about" - tomgee; 10 May 2006 PWNED -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ "Puddlefuck tou are on my kill file. Good bye" - Vert admits he cannot calculate \gamma for a photon and admits defeat - 2nd July 2006 PWNED -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
From: Ka-In Yen on 9 Jul 2006 21:05 Ka-In Yen wrote: > Eric Gisse wrote: > > You repost the same tripe about once a month in the same thread over > > and over while ignoring criticisms that would cause you to have to > > abandon your work. > > Home work for Eric Gisse: > A rectangle sits in 3D space. The area vector of the rectangle is A, > and the legth vector of one side of the rectangle is L. Please find > the length vector of the other side of the rectangle? Dear Eric Gisse, How long do you need to solve this problem? I am waiting for your answer. You can discuss with Bilge and Puddleduck, if the problem is difficult.
From: Phineas T Puddleduck on 9 Jul 2006 21:06 On 10/7/06 02:05, in article 1152493510.006042.208350(a)p79g2000cwp.googlegroups.com, "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote: > Dear Eric Gisse, > > How long do you need to solve this problem? I am waiting > for your answer. You can discuss with Bilge and Puddleduck, > if the problem is difficult. Why should any of us waste our time with your BS? -- Relf's Law? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ "Bullshit repeated to the limit of infinity asymptotically approaches the odour of roses." Corollary -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ?It approaches the asymptote faster, the more ?pseduos? you throw in your formulas.? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ Jaffa cakes. Sweet delicious orange jaffa goodness, and an abject lesson Why parroting information from the web will not teach you cosmology. -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ Official emperor of sci.physics, head mumbler of the "Cult of INSANE SCIENCE". Pay no attention to my butt poking forward, it is expanding. -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
From: Bilge on 10 Jul 2006 06:07
Ka-In Yen: > >Ka-In Yen wrote: >> Eric Gisse wrote: >> > You repost the same tripe about once a month in the same thread over >> > and over while ignoring criticisms that would cause you to have to >> > abandon your work. >> >> Home work for Eric Gisse: >> A rectangle sits in 3D space. The area vector of the rectangle is A, >> and the legth vector of one side of the rectangle is L. Please find >> the length vector of the other side of the rectangle? > >Dear Eric Gisse, > >How long do you need to solve this problem? I am waiting >for your answer. You can discuss with Bilge and Puddleduck, >if the problem is difficult. The problem is that you are wrong. Since only you can correct that problem, it will be impossile for anyone but you to solve. Please continue waiting. |