# Eigenvalues and the Principal Invariants of a Linear Map

Eigenvalues and the Principal Invariants of a Linear Map

The quantities =tr(A), =-tr(), =det(A) are called the principal invariants of the matrix .

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tr(A)

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Drag the point in the - plane and move the slider to display the corresponding eigenvalues around the unit circle in the complex plane.

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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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