Which matrix decomposition of a centered data matrix yields the principal component directions as its right singular vectors?

Singular Value Decomposition

Singular Value Decomposition (SVD) factorizes a matrix into three distinct components, where the right singular vectors represent the axes of maximum variance in the dataset. This mathematical technique is the engine behind Principal Component Analysis (PCA), allowing for efficient dimensionality reduction by identifying the most important patterns in data. A helpful way to remember this is that SVD is often called the 'Swiss Army Knife' of linear algebra because it can be applied to any matrix, regardless of its shape.