What is Principal Component Analysis (PCA) and what does it mathematically optimize?

Question

Data Science with Python — Hard

What is Principal Component Analysis (PCA) and what does it mathematically optimize?

Accepted Answer

Principal Component Analysis (PCA) is a dimensionality reduction technique that identifies orthogonal axes of maximum variance in data. By computing eigenvectors of the covariance matrix, PCA projects data onto a lower-dimensional subspace while preserving the most variance.