How to partition a matrix into components that are independent?

I'm going to partition a symmetric matrix (covariance matrix) into columns/rows that are independent. Any help is appreciated.

[Mahdi]

Do you mean that you want to extract certain values (rows/columns) and define them as new variables?

[MJ]

No. I have a symmetric matrix, a covariance matrix (40x40), which includes linearly dependent variables. I'm going to find variables that are linearly correlated, or those that are independent.

Answer 1

[Star Strider]

Is this what you want to do?

X = rand(4,4);
Xr = X(2,:)         % Extract second row
Xc = X(:,3)         % Extract third column

[MJ]

No. I have a cov matrix (40x40) that includes several linearly dependent variables, so I'm trying to find those variables.

[Star Strider]

The easiest way is probably to use the core MATLAB function corrcoef. The way I would suggest using it is to use the P (probability) values:

[R,P] = corrcoef(X)
[pr,pc] = find(P < 0.05)

and search for the lowest ones, or those that exceeded your limits, for instance P < 0.05 or lower. The find function will give you the row and column indices for those values. There may be other criteria, but this has the advantage of having statistical validity.

Answer 2

[Kelly Kearney]

help corr

Will calculate linear correlation between columns of a matrix.