Thread: Can this matrix be ...

Fmatrix.gif

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

Originally Posted by ReMakeIt

Fmatrix.gif

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

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 X₁^TX₂ instead of (X₁-X₂)²

Originally Posted by ReMakeIt

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 X₁^TX₂ instead of (X₁-X₂)²

Like I said, I'm not sure that this is possible since all the x are different vectors.
Not sure how to go about this.

in matrix form







Mass matrix M and acceleration matrix A:

;

And

Originally Posted by ReMakeIt

in matrix form







Mass matrix M and acceleration matrix A:

;

And

Is this not different from the original matrix? I don't see the cube factors coming into this.
Also, where is the differential operator ? These aren't differential equations any more.