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
