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Vai
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Homework Statement
So I'm working on this proof. Given an n x n (square) matrix, prove that it's determinant is equal to the product of it's singular values.
Homework Equations
We are given A = U*E*V as a singular value decomposition of A.
The Attempt at a Solution
I was thinking that det(A) = det(U) * det(E) * det(V)
and since E is the diagonal matrix with singular values on it's diagonal, it's determinant is the product of those singular values.
But then what to do about det(U) and det(V)? I guess it's logical that the product of their determinants is 1, but how do I show that?