Not just 2 equations and 2 functions: any number of (linear ordinary)
differential equations of any order (with constant coefficients) are
solved with vectors of complex numbers.
Henry Rich
On 12/17/2013 11:32 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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@@i = Arie Groeneveld
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