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The Perron-Frobenius theorem states that for a square matrix with all positive entries, there is a unique largest real eigenvalue and that its corresponding eigenvector has positive x and y coordinates.

For example, a bit flip on the first qubit will result in the measured eigenvalue of becoming −1.

An engineer could then use a technique called eigenvalue analysis to investigate the stability of the bicycle as one might do with an aeroplane design.

The amount by which a unit length segment pointing in this direction is stretched or shrunk is the eigenvalue.