The absolute values |Eox| and |Eoy| (as stated in your reference)
themselves make a single 2D vector which has an Euclidian norm.
A similar but simpler problem is the field under a long (z-directed)
multiphase transmission line. For AC at 60Hz, , phasor values of line
voltages are used ( a quasi electrostatic model is more than adequate
) and at a given point the magnitude and phase of Ex and Ey can be
found. Since |Ex| and |Ey| are rms values, the Euclidean norm of these
is the rms value of the total field. Direction and strength of e(t)
information is lost but typically Ex and Ey are not in phase so one
could consider the e(t) as being polarized- which appears to be what
Jones is dealing with.
I believe that, in this case the application was looking for a distance
and the verb en that was given purported to do this
In this case the results given for 2 vectors in a 2D world gave the same
result as a 4D vector in a 4D world.
In other words the verb when given 1j1 and 1j1 as arguments, gives a
result of 2 !!. (the same as the result for 1,1,1,1 in a 4D world where
it makes sense)..
Don
On 20/12/2013 6:13 AM, Bo Jacoby wrote:
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
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