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== Overview ==
When performing PCA, the first principal component of a set of <math>p</math> variables is the derived variable formed as a linear combination of the original variables that explains the most variance. The second principal component explains the most variance in what is left once the effect of the first component is removed, and we may proceed through <math>p</math> iterations until all the variance is explained. PCA is most commonly used when many of the variables are highly correlated with each other and it is desirable to reduce their number to an [[linear independence|independent set]].
The first principal component can equivalently be defined as a direction that maximizes the variance of the projected data. The <math>i</math>-th principal component can be taken as a direction orthogonal to the first <math>i-1</math> principal components that maximizes the variance of the projected data.
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