>
> A brief description is - the sqrt(matrix determinant) is not equal to the
> product of the eigenvalues of matrix**(1/2).
>
> Could you please help a little bit in there...? Would what I am doing even
> be mathematically correct?
>
>>> var('a:d')
(a, b, c, d)
>>> m=Matrix(2,2,[a,b,c,d])
>>> m.det()
a*d - b*c
>>> m.eigenvals()
{a/2 + d/2 - sqrt(a**2 - 2*a*d + 4*b*c + d**2)/2: 1, a/2 + d/2 + sqrt(a**2
- 2*a*d + 4*b*c + d**2)/2: 1}
>>> Mul(*_).simplify()
a*d - b*c
>>> m3=Matrix(3,3,var('x:9'))
>>> d=m3.det()
>>> e=Mul(*m3.eigenvals()).simplify()
>>> d==e
True
Does someone have the identity wrong? above it appears that det(M) =
Mul(*M.eigenvals())
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