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Game Cards — Chapter 6
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Power iteration
Power iteration converges to the dominant eigenvector when the largest eigenvalue in magnitude is separated.
Inverse iteration
Inverse iteration with a shift targets eigenvalues close to the shift.
SVD link
Singular values reveal rank, conditioning, and geometric stretching.
Rayleigh quotient
The Rayleigh quotient gives an eigenvalue estimate from a candidate vector.
Eigenvalue problem
An eigenpair satisfies \(Av=\lambda v\). Eigenvalues encode modes, frequencies, growth/decay, and stability.
QR iteration
QR iteration preserves eigenvalues through similarity transformations and reveals them in triangular or diagonal form.