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Linear Algebra
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Eigenvalues & eigenvectors
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660.
Rank from Eigenvalues
medium
A covariance matrix has eigenvalues [10, 3, 0.5, 0.1]. What is the rank of this matrix?
A
4, since all four eigenvalues are nonzero indicating four linearly independent directions
B
1, since the largest eigenvalue dominates and the others are negligible by comparison
C
0, since the eigenvalues are not integers and rank requires counting whole independent directions
D
3, since only three eigenvalues exceed 1, indicating three meaningful directions
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