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The PCA algorithm subtracts the mean from the data to centralize it, meaning that the mean of all points should be zero. This step prepares the data for the variance-based step that follows, making the formula for the scatter matrix simpler.

Conditions: The data must first be represented as a matrix X.; The subtraction is by the mean $\overline{X}$.; After this step, the video uses $\overline{X} = 0$ in the scatter-matrix discussion.

The PCA algorithm subtracts the mean from the data to centralize it, meaning that the mean of all points should be zero. This step prepares the data for the variance-based step that follows, making the formula for the scatter matrix simpler.

Conditions: The data must first be represented as a matrix X.; The subtraction is by the mean $\overline{X}$.; After this step, the video uses $\overline{X} = 0$ in the scatter-matrix discussion.