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
