Find PC1 by rotating the axis

Why this lab Find PC1 yourself by rotating an axis through the data.

Your job is not to recall a definition. Rotate the candidate component until the projected scores spread out as much as possible. That maximum-variance direction is the first principal component.

In matrix terms. The direction you are searching for is the first eigenvector of the covariance matrix of the centered data — of the correlation matrix once the variables are standardized. The variance of the scores along it is the largest eigenvalue, \( \lambda_1 \), which is the target printed beside the meter.