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AI & ML · Machine Learning Math

PCA & SVD

128 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    PCA on a dataset yields covariance eigenvalues λ1=6\lambda_1 = 6, λ2=4\lambda_2 = 4, λ3=1\lambda_3 = 1. What fraction of the total variance is explained by the first principal component?

  2. Warm-up

    PCA on a dataset yields covariance eigenvalues λ1=7\lambda_1 = 7, λ2=4\lambda_2 = 4, λ3=2\lambda_3 = 2. What fraction of the total variance is explained by the first principal component?

  3. Warm-up

    PCA on a dataset yields covariance eigenvalues λ1=9\lambda_1 = 9, λ2=2\lambda_2 = 2, λ3=1\lambda_3 = 1. What fraction of the total variance is explained by the first principal component?

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