# principal component analysis (proof)

(45 minutes to learn)

## Summary

The proof that principal component analysis (PCA) finds the subspace maximizing the variance and minimizing the reconstruction error.

## Context

This concept has the prerequisites:

- principal component analysis
- variational characterization of eigenvalues (Justifying PCA depends on the formulation of eigenvalues as an optimization problem.)

## Core resources (read/watch one of the following)

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Sections 12.1.1-12.1.2, pages 561-565

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 12.2.2, pages 389-391

## See also

-No Additional Notes-