Prove that for in H,
Thus, N is a homomorphism from onto the positive real numbers.
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We can solve this problem in several ways: we could check directly that the relations hold, or in order to simplify the computations we can use the other problem (that I already solved) that was included in this set of problem, that said that to any a in H we can associate a matrix A_a, which we showed that has the properties that det(A_a)=N(a)^2 (I will use the notation x^2 for the square of x), and ...
This is a proof regarding a homomorphism onto positive real numbers.