# Comparison of matrixes

## Main Question or Discussion Point

Hello everybody!

I have a large set of items and, two-by-two, there exists some kind of attraction/repulsion that I have measured. I synthesize this information in a (nxn) matrix.
Under different circumstances this attraction/repulsion changes.

So, what kind of statistical/mathematical procedure can I use to measure whether the changes (for the whole set) are “large/small”, as well as if a subset of them (lets say the first ten items) the attraction is larger than in another subset (lets say the last ten items)?.

Perhaps provide some sample data to help us understand what you are trying to get at?

My data are comprised in different matrices (each of the situations provide that information).
First one
x 1.3 -1.5 . . . . . .
1.3 x 1.2 . . . . . .
-1.5 1.2 x . . . . . .
. . . . . . . . . . . . . .

Second one
x 1.1 1.3 . . . . . .
1.1 x -0.2 . . . . . .
1.3 -0.2 x . . . . . .
. . . . . . . . . . . . . . .

Third one
x -0.1 0.3 . . . . . .
-0.1 x 0.4 . . . . . .
0.3 0.4 x . . . . . .
. . . . . . . . . . . . . . .

All of them are symmetrical and the diagonal does not make sense (I could write any number). Note that the dimension will be around 300 x 300 for each matrix.

How can I say if first one is closer (and how closer is) to second one than to third one (as well as any other combination)?

Thanks again.

My data are comprised in different matrices (each of the situations provide that information).
First one
x 1.3 -1.5 . . . . . .
1.3 x 1.2 . . . . . .
-1.5 1.2 x . . . . . .
. . . . . . . . . . . . . .

Second one
x 1.1 1.3 . . . . . .
1.1 x -0.2 . . . . . .
1.3 -0.2 x . . . . . .
. . . . . . . . . . . . . . .

Third one
x -0.1 0.3 . . . . . .
-0.1 x 0.4 . . . . . .
0.3 0.4 x . . . . . .
. . . . . . . . . . . . . . .

All of them are symmetrical and the diagonal does not make sense (I could write any number). Note that the dimension will be around 300 x 300 for each matrix.

1) How can I say if first one is closer (and how closer is) to second one than to third one (as well as any other combination)?
2) I care about an external condition, that is the same for all the pairs that generate the matrix (so, it has a single value for all the pairs in the matrix) , and I would like to know if the proximity could be related to that condition.

Thanks again.

I don't really get what you are trying to do with the matrices, but from what I understand:

(1) the matrices are symmetric

(2) only the off-diagonal components are important.

(3) they swing between negative and positive values.

Let me suggest some ideas? you could take the off-diagonal components and put them in a vector instead. Then instead of comparing 2 matrices, you compare 2 vectors.

Take the difference of the two vectors and call it the residual vector. If some entries are more important than others you can multiply each entry in the residual vector by different weights (assigned arbitrarily of course). Then take the modulus of this residual vector.

CRGreathouse