# Deriving the second principal component

> ML preparation item.

- Stable ID: `pml-book1-ex20.3`
- Area: Machine Learning
- Topic: Dimensionality Reduction
- Origin: external
- Expected time: 18 minutes
- Skills: pca-objective, covariance-eigendecomposition
- Item JSON: https://mlprep.iwase.dev/data/items/pml-book1-ex20.3.json

This site does not reproduce the third-party problem.

- Source: Probabilistic Machine Learning: An Introduction — online draft dated 2025-04-18
- Document: PML Book 1 online draft (2025-04-18), Chapter 20 exercises
- Locator: Exercise 20.3, book p. 712 (PDF p. 742)
- Official answer PDF page(s): 40–41
- Original problem: https://github.com/probml/pml-book/releases/download/2025-04-18/book1.pdf#page=742
- Official answer: https://probml.github.io/pml-book/solns-public.pdf#page=40
- Answer status: official-solution
- Source caveat: The public solution manual predates the dated book draft; the exercise title and task align, but notation may differ.


## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `pml-book1-ex20.3`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.