The Determinant Using Traces

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.

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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 Student Mathematica Contest.
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