Eigenvalues and the Principal Invariants of a Linear Map

The quantities , , are called the principal invariants of the matrix .
Drag the point in the - plane and move the slider to display the corresponding eigenvalues around the unit circle in the complex plane.
In the left-hand graphic, the discriminant is negative in the purple region; in the orange region, the eigenvalues have modulus less than one.
The eigenvalues of the matrix determine how the flow of a differential map or the orbit of a discrete map behaves.

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