# Determining the hamiltonian

1. Nov 3, 2012

### aaaa202

My book writes a 5-step recipe for detemining the hamiltonian, which I have attached. However I see a problem with arriving at the last result. Doesn't it only follow if the matrix M is a symmetric matrix - i.e. the transpose of it is equal to itself.

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2. Nov 4, 2012

### praharmitra

I am assuming the tilde above an object implies taking a transpose. If that is the case, then M is indeed a symmetric matrix. One can see this by looking at the Lagrangian. Since the Lagrangian is a number, we can take a transpose of L and we'll get back the same number, i.e. $L^T=L$, this will rewrite the Lagrangian in terms of $M^T$. But since these are equal, we must have $M^T=M$