PCA input matrix dimensions

Hi,

The formula for PCA is X=UV, where X is a pxn matrix (columns: observations; rows: variables), U (the coeff matrix) is a pxp matrix, and V (scores) is a pxn matrix. However, in Matlab the input should be transposed (this is, a nxp matrix, where columns are the variables, and not observations). I wonder why the consistency of the original formula was changed. Thank you.

[Walter Roberson]

https://en.wikipedia.org/wiki/Principal_component_analysis#Details describes,

"Consider a data matrix, X, with column-wise zero empirical mean (the sample mean of each column has been shifted to zero), where each of the n rows represents a different repetition of the experiment, and each of the p columns gives a particular kind of feature (say, the results from a particular sensor)."

That is columns as variables and rows as observations, the same order that MATLAB uses.

[Tahariet Sharon]

Thanks you, Walter. So if X is time x sensors, then COEFF is time x PCs?