Eigenvalues and the Principal Invariants of a Linear Map

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


Contributed by: George Shillcock (March 2019)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.