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