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Let n be the number of observations and p the number of variables involved in the multivariate analysis of interest. Denote the n by p matrix of data values by X.
The SVD is usually applied to standardized data. To standardize a value, subtract its mean and divide by its standard deviation. Denote the n by p matrix of standardized data values by Xs. Then the covariance matrix of the standardized data is the correlation matrix for X and is given as follows:
The SVD can be applied to Xs to obtain the eigenvectors and eigenvalues of Xs’Xs. This allows efficient calculation of eigenvectors and eigenvalues when the matrix X is either extremely wide (many columns) or tall (many rows). This technique is the basis for Wide PCA. See Principal Components Report in Principal Components.

Help created on 3/19/2020