See https://en.wikipedia.org/wiki/Jones_calculus for an application of 2D complex vectors and their euclidean norms.
Den 15:07 fredag den 20. december 2013 skrev km <[email protected]>: "I don't think the Euclidian norm applies in this case [a vector of two complex numbers]. If so, please let me know how. Don" > >I don't know how without knowing the application. Besides the Euclidian norm >there are the taxicab norm (sum of absolute values) and sup norm (maximum of >absolute values) which may be of more use in a given application. > >A possible application for two complex numbers is that the first is position >and the second is velocity. Their individual Euclidian norms are distance >from the origin and speed. The Euclidian norm of the pair might be an >indicator of fuel cost for getting to the origin; if we're talking about a >taxicab, the taxicab norm might be more useful! > >For what it's worth, there is a mathematical definition of "norm in a vector >space", and the Euclidian, taxicab, and sup norms all satisfy that definition. > >--Kip Murray > >Sent from my iPad > >> On Dec 20, 2013, at 6:37 AM, EelVex <[email protected]> wrote: >> >> You can apply an Euclidian norm in any n-dimensional space you like. >> What do you mean it might not apply in this case? >> >> >> >>> On Fri, Dec 20, 2013 at 6:02 AM, Don Kelly <[email protected]> wrote: >>> >>> I have little problem with complex numbers, having used them for the last >>> 70 years and surviving math and other grad courses dealing with them (at U >>> of Alberta, U of Illinois -Champlain Urbana) where I struggled through a >>> PhD in EE >>> I also have dealt with (complex number ) matrices considerably larger than >>> 2 by 2 and with higher order sets of differential equations, In both cases, >>> nonlinearity lifts its ugly head. Hey, when dealing with power systems and >>> machines, big messy problems exist . >>> >>> My problem is not with complex numbers but with the verb 'en' which works >>> with any single vector. but if you give it 2 -2D vectors (i.e complex >>> numbers) it treats the components of the two vectors (say 1j2 , 4j10) as if >>> they are a single 4D vector. >>> I really don't think the Euclidian norm applies in this case. If so, >>> please let me know how. >>> >>> Don >>> >>> >>> >>> >>> >>> >>>> On 17/12/2013 8:32 PM, km wrote: >>>> >>>> There are uses for such vectors, along with 2 by 2 matrices of complex >>>> numbers, in the theory and practice of two differential equations with two >>>> unknown functions. This is the kind of math engineers usually learn in >>>> their third year of college or university. Certain problems become easier >>>> to do when you use complex numbers and matrices. Today's software takes >>>> away most of the drudgery! >>>> >>>> I have to admit that in second year courses complex numbers and matrices >>>> tend to be Chapter 10 of a ten-chapter book, for example Gilbert Strang's >>>> Introduction to Linear Algebra, used in sophomore courses at MIT and at my >>>> school the University of Houston. >>>> >>>> --Kip Murray >>>> >>>> Sent from my iPad >>>> >>>>> On Dec 17, 2013, at 8:52 PM, Don Kelly <[email protected]> wrote: >>>>> >>>>> I have some problem here with the 2D complex vector. >>>>> Either 1j2 and 4j10 are vectors (2D) measured from the origin OR they >>>>> specify a vector in terms of two end points. >>>>> In the first case they each have independent norms 1.414 and 2.236 as >>>>> given by (|) >>>>> In the second case the vector is,for example, the difference (+/-) >>>>> 3j8which has a norm 8.544 >>>>> when en produces the same result for a 4D vector 1 2 4 10 and for 2 2D >>>>> vectors, we are somehow sending one of these into the third and fourth >>>>> dimensions. >>>>> >>>>> My problem is that a norm is defined for each of the vectors and or the >>>>> vector result of operations on these vectors. en appears to be work for >>>>> a single vector in any dimensional space but the Euclidean norm is a >>>>> measure of the length of an individual vector- not of two independent >>>>> vectors in the same space. >>>>> >>>>> Don Kelly >>>>> >>>>>> On 16/12/2013 7:24 AM, Bo Jacoby wrote: >>>>>> NB. I would omit ("1) and arrange multiple vectors in columns. >>>>>> en =: [: %: [: +/(* +) >>>>>> ]zz =: |: 2 2 $ 1j1 1j1 1j2 4j10 NB. two column vectors >>>>>> 1j1 1j2 >>>>>> 1j1 4j10 >>>>>> en 1 2 4 10 NB. norm of 4D real vector >>>>>> 11 >>>>>> en 1j2 4j10 NB. 2D complex vector >>>>>> 11 >>>>>> en zz NB. norms of column vectors >>>>>> 2 11 >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> Den 15:42 mandag den 16. december 2013 skrev Lippu Esa < >>>>>> [email protected]>: >>>>>> Very nice indeed! >>>>>> >>>>>>> Esa >>>>>>> -----Original Message----- >>>>>>> From: [email protected] [mailto: >>>>>>> [email protected]] On Behalf Of Aai >>>>>>> Sent: 16. joulukuuta 2013 14:42 >>>>>>> To: [email protected] >>>>>>> Subject: Re: [Jprogramming] Length of a vector >>>>>>> >>>>>>> |@j./"1 yy >>>>>>> 5 13 >>>>>>> 17 25 >>>>>>> >>>>>>> >>>>>>>> On 16-12-13 04:38, km wrote: >>>>>>>> This is an easy one, but let's see what you come up with. >>>>>>>> >>>>>>>> The Euclidian norm or length of a vector is the square root of the >>>>>>>> sum of the squares of its components. Write verb en below. It >>>>>>>> should be >>>>>>>> able to find the length of a vector of any number of components. >>>>>>>> >>>>>>>> ]yy =: 2 2 2 $ 3 4 5 12 8 15 7 24 >>>>>>>> 3 4 >>>>>>>> 5 12 >>>>>>>> >>>>>>>> 8 15 >>>>>>>> 7 24 >>>>>>>> en yy NB. lengths of 3 4 and 5 12 and 8 15 and 7 24 >>>>>>>> 5 13 >>>>>>>> 17 25 >>>>>>>> >>>>>>>> -- Kip Murray >>>>>>>> >>>>>>>> Sent from my iPad >>>>>>>> ------------------------------------------------------------ >>>>>>>> ---------- >>>>>>>> For information about J forums see http://www.jsoftware.com/ >>>>>>>> forums.htm >>>>>>>> >>>>>>> -- >>>>>>> Met vriendelijke groet, >>>>>>> @@i = Arie Groeneveld > >>>>>>> >>>>>>> >>>>>>> ---------------------------------------------------------------------- >>>>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>>>> ---------------------------------------------------------------------- >>>>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>>>> >>>>>> ---------------------------------------------------------------------- >>>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>>> >>>>> ---------------------------------------------------------------------- >>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
