The Determinant Using Traces
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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
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.