WOLFRAM|DEMONSTRATIONS PROJECT

The Determinant Using Traces

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matrix size
2
3
4
5
6
7
8
9
10
assume traceless
A-
1
144
Tr[
3
A
]
3
Tr[
2
A
]
+
1
40
Tr[
5
A
]
2
Tr[
2
A
]
+
1
24
Tr[
3
A
]Tr[
4
A
]Tr[
2
A
]-
1
14
Tr[
7
A
]Tr[
2
A
]+
1
162
3
Tr[
3
A
]
-
1
20
Tr[
4
A
]Tr[
5
A
]-
1
18
Tr[
3
A
]Tr[
6
A
]+
Tr[
9
A
]
9
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.