As I sit here listening to the giant "whoosh" sound of all the world's
biologists unsubscribing from the CCP4BB, I wonder if anyone on this
thread can explain to me the difference between a matrix and a tensor?
I ask because I think stress and strain are mechanisms of radiation
damage, but where I am stuck is that Young's modulus seems to always be
represented by a "tensor" (as opposed to something that makes sense).
This is not helped by the lack of a tensor class in stdlib!
However, I do think it is interesting that this same Thomas Young
performed a famous experiment in 1801 that (eventually) proved a single
photon can scatter off of two slits at the same time. This is one of
two experiments that can only be explained by quantum mechanics.
-James Holton
stressed and strained scientist
On 10/14/2010 8:22 AM, Ed Pozharski wrote:
Again, definitions are a matter of choice. Under your strict version I
still may consider electric current as vector, if I introduce the
coordinate system in the circuit. When I transform the coordinate
system (from clockwise to counterclockwise), current changes direction
with it. By the way, check the *current density* - it is a vector and
it obeys, in generalized case of an inhomogeneous material, a tensor
form of Ohm's law.
There is no "correct" definition of anything. Ian is right in the
narrow sense of the conventional vector in multiple dimensions and,
especially, regarding the software implementation. But there is a
legitimate (i.e. not self-contradictory) broader definition of a vector
as an element of vector space, and complex numbers fall under it. Math
is flexible, and there is definite benefit of consider complex numbers
(and electric current under some circumstances) as vectors.
Checking out of semantics hotel,
Ed.
On Thu, 2010-10-14 at 16:47 +0200, Ganesh Natrajan wrote:
The definition of a vector as being something that has 'magnitude' and
'direction' is actually incorrect. If that were to be the case, a
quantity like electric current would be a vector and not a scalar.
Electric current is a scalar.
A vector is something that transforms like the coordinate system, while
a scalar does not. In other words, if you were to transform the
coordinate system by a certain operator, a vector quantity in the old
coordinate system can be transformed into the new one by using exactly
the same operator. This is the correct definition of a vector.
G.
On Thu, 14 Oct 2010 10:22:59 -0400, Ed Pozharski
<epozh...@umaryland.edu> wrote:
The definition game is on! :)
Vectors are supposed to have direction and amplitude, unlike scalars.
Curiously, one can take a position that real numbers are vectors too, if
you consider negative and positive numbers having opposite directions
(and thus subtraction is simply a case of addition of a negative
number). And of course, both scalars and vectors are simply tensors, of
zeroth and first order :)
Guess my point is that definitions are a matter of choice in math and if
vector is defined as an array which must obey addition and scaling rules
(but there is no fixed multiplication rule - regular 3D vectors have
more than one possible product), then complex numbers are vectors. In a
narrow sense of a real space vectors (the arrow thingy) they are not.
Thus, complex number is a Vector, but not the vector (futile attempt at
using articles by someone organically suffering from article dyslexia).
Cheers,
Ed.
O
