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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.


	Contributed by: Oleksandr Pavlyk
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Consider the polynomial

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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