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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.


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.


"The Determinant Using Traces" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/TheDeterminantUsingTraces/
Contributed by: Oleksandr Pavlyk
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