The eigenvectors and eigenvalues of a covariance (or correlation) matrix represent the “core” of a PCA: The eigenvectors (principal components) determine the directions of the new feature space, and the eigenvalues determine their magnitude.

What does an eigenvector represent?

Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed.

What is Eigen value in PCA?

Eigenvalues are coefficients applied to eigenvectors that give the vectors their length or magnitude. So, PCA is a method that: Measures how each variable is associated with one another using a Covariance matrix. Understands the directions of the spread of our data using Eigenvectors.