Correlation matrix

The standardized version of the Covariance Matrix.

The general layout is the same as that of the covariance matrix, but here, entry C[i, j] is the correlation coefficient of (x_i, x_j) (instead of their covariance).

So the diagonal has now "1" in all positions (the value of the correlation coefficient of a variable with istself), and off-diagonal positions (i, j) are r(x_i, x_j) (or r(x_i, x_j)), the correlation coefficient of variables x_i and x_j. The matrix is of course symmetrical.

Whereas the covariance matrix is of prime interest to the theoretician, practitioners are more used to the correlation matrix, because of correlation coefficient is more intuitive than a covariance. Other than that, both matrices have essentially the same properties ().

Principal Components Analysis is performed by diagonalization of the Correlation Matrix of the variables (usually, after they have been standardized).

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Related readings :

Covariance matrix
Correlation coefficient
Principal Components Analysis

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The general layout is the same as that of the covariance matrix, but here, entry C[i, j] is the correlation coefficient of (xi, xj) (instead of their covariance).

The general layout is the same as that of the covariance matrix, but here, entry C[i, j] is the correlation coefficient of (x_i, x_j) (instead of their covariance).