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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
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
.
RELATED LINKS
Determinant
(
Wolfram
MathWorld
)
Matrix Trace
(
Wolfram
MathWorld
)
Our First Russian Student Competition
(
Wolfram Blog
)
PERMANENT CITATION
"
The Determinant Using Traces
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheDeterminantUsingTraces/
Contributed by:
Oleksandr Pavlyk
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