[Jprogramming] Length of a vector

[km]

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 <dhky at shaw.ca> 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 <Esa.Lippu at varma.fi>:
>>  Very nice indeed!
>>> Esa
>>> -----Original Message-----
>>> From: programming-bounces at forums.jsoftware.com [mailto:programming-bounces at forums.jsoftware.com] On Behalf Of Aai
>>> Sent: 16. joulukuuta 2013 14:42
>>> To: programming at jsoftware.com
>>> 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
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>>> -- 
>>> Met vriendelijke groet,
>>> @@i = Arie Groeneveld
>>> 
>>> 
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