The Determinant Using Traces

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 determinant of a square matrix can be computed as a polynomial of traces of the matrix and its powers. This expression greatly simplifies for traceless matrices.

Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Consider the polynomial in of degree , where is the identity matrix. Its leading coefficient is .

On the other hand,

.

Comparing coefficients in the powers of λ gives .

This derivation is due to Vladimir Dudchenko, the first prize winner of the Russian StudentMathematicaContest.



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.
Send