- #1

Vai

- 5

- 0

## 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?