Fmatrix.gif
Can this 10x10 matrix be represented as the the outer product of two vectors?

Last edited by ReMakeIt; February 6th, 2012 at 01:31 AM.
You can pull the mass factors m out into a vector, but the x will be a major problem because of the cube factor. I'm sure it can be done somehow ( binomial expansion ? ) but the result will be very ugly from an algebraic point of view. Do you have access to a computer algebra system like Mathematica or Maple ? You could try that way.
Is there some way to factor the vector X out of this?
x1 = \vect{x}
x2
x3
.
.
.
.
x10
ick the attachment looks like that?
I dont have a computer to do the dirty work. The vectors should make some sort of physical sense don't you think? Perhaps I need to look at the vector
X(r, Phi, theta)
r1 phi1 theta1
r2 phi2 theta2
...
...
...
r10 phi10 theta10
Somehow that division of magnitude squared and pointer should fall out...
Magnitude can be written X_{1}^{T}X_{2} instead of (X_{1}X_{2})^{2}
in matrix form
Mass matrix M and acceleration matrix A:
;
And
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