Which is an accurate statement about the eigenvectors in PCA?

In Principal Component Analysis (PCA), eigenvectors play a key role in identifying the directions in which the data varies the most. Each eigenvector corresponds to a principal component, and these directions are determined by the eigenvectors of the covariance matrix of the data. The principal components are essentially the axes along which the variation in the data is maximized, making option B a true statement.

While eigenvectors are related to the variance in data (each eigenvalue associated with an eigenvector represents the magnitude of variance along that direction), it is the eigenvectors themselves that indicate the direction of these principal components. Consequently, this nuance clarifies why the focus on direction makes option B accurate.

Normalization of eigenvectors is not a requirement for them to function effectively in PCA; they inherently represent the essential characteristics of the data. Therefore, statements about normalization do not necessarily reflect an intrinsic property of the eigenvectors in the context of PCA.