How to partition a matrix into components that are independent?

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MJ 2014-5-26

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https://ww2.mathworks.cn/matlabcentral/answers/131205-how-to-partition-a-matrix-into-components-that-are-independent

评论： Star Strider 2014-5-26

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

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Mahdi 2014-5-26

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

MJ 2014-5-26

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.

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Answer 1

Star Strider 2014-5-26

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https://ww2.mathworks.cn/matlabcentral/answers/131205-how-to-partition-a-matrix-into-components-that-are-independent#answer_138323

在 MATLAB Online 中打开

Is this what you want to do?

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

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MJ 2014-5-26

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

Star Strider 2014-5-26

在 MATLAB Online 中打开

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.

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