# Connect SVD to PCA

> ML Prep screening item.

- Stable ID: `ml-screen-dimensionality-standard-svd`
- Collection: screening
- Area: Machine Learning
- Topic: Dimensionality Reduction
- Origin: original
- Difficulty: medium
- Expected time: 8 minutes
- Skills: covariance-eigendecomposition, pca-via-svd, explained-variance
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-dimensionality-standard-svd.json

## Problem

For the centered matrix

$$
X=\begin{bmatrix}2&0\\0&1\\-2&0\\0&-1\end{bmatrix},
$$

compute $X^{\mathsf T}X$, the singular values, the first PCA direction, and the first-component explained-variance fraction.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

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