What is the relationship between PCA and SVD geometrically?

SVD decomposes data into orthogonal axes that correspond to PCA components.

PCA can be computed using Singular Value Decomposition of the centered data matrix X = UΣVᵀ. The columns of V represent principal directions, while singular values in Σ represent the amount of variance captured. Geometrically, SVD rotates and scales the data into orthogonal axes aligned with maximum variance directions.