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GATE 2026 DA – Question 11

Machine Learning · Dimensionality reduction and principal component analysis · 1 mark · Multiple choice

For a classification problem, Principal Component Analysis (PCA) has been used to reduce the dimensionality of a feature space from 100 to 10.

Which of the following options is true about the angle $\theta$ between the first and the tenth principal components?

  1. $\theta = 0^\circ$
  2. $\theta = 90^\circ$
  3. $90^\circ < \theta \le 180^\circ$
  4. $0 < \theta < 90^\circ$

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Show answer and explanation

Correct answer: (B) $\theta = 90^\circ$

Explanation

The principal components are the eigenvectors of the covariance matrix, which is symmetric. Eigenvectors of a symmetric matrix that belong to different eigenvalues are orthogonal, and PCA picks the components to be orthogonal in any case. So the angle between any two different components is 90°.