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Maths · Module 3Module material

Matrices interview questions

15 questions interviewers ask on this module’s topics, from first principles to the follow-ups. Each comes with a model answer.

  1. Give two ways to read a matrix–vector product.
  2. What is the shape rule for A @ B?
  3. What does a 2 × 2 matrix do to the plane, and how do you read it?
  4. What does the determinant measure?
  5. Why is AB not BA, and which acts first?
  6. What is (AB)⁻¹?
  7. How do you tell whether a matrix is close to singular?
  8. You add a temperature column in Fahrenheit to data that already has Celsius. What happens to linear regression?
  9. Derive the normal equations.
  10. Why do libraries not solve linear regression with inv(X.T @ X)?
  11. What is an eigenvector, and when are a matrix's eigenvectors perpendicular?
  12. Why is gradient descent slow on unscaled features?
  13. What is the SVD, and how is it related to the eigendecomposition?
  14. How does PCA relate to the SVD and the covariance matrix?
  15. What is the difference between np.cov(X) and np.cov(X, rowvar=False, bias=True)?