Practice question · Match the pairs
Match each eigenvalue application to its field.
- Leontief input-output
- Dynamic stability
- PCA
- Markov chains
- Stationary distribution is the eigenvector for eigenvalue 1
- Dominant eigenvalue determines net surplus feasibility
- Eigenvectors of covariance matrix are principal components
- Eigenvalue magnitudes determine convergence or explosion
Hints
- Each field uses the same idea for a different purpose.
- One application finds the direction of greatest variance.
Show the answer
- Leontief input-output → Dominant eigenvalue determines net surplus feasibility
- Dynamic stability → Eigenvalue magnitudes determine convergence or explosion
- PCA → Eigenvectors of covariance matrix are principal components
- Markov chains → Stationary distribution is the eigenvector for eigenvalue 1
Why
Eigenvalues answer the same question across economics, statistics, and dynamics: what are the system's natural directions and rates?
Practise Eigenvalues and Eigenvectors
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