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An approach to define the entanglement between identical particles, is to use the so-called geometric idea. For example, the generic wave function of a fermionic system is not a Slater determinant. However, since the simplest wave function for a fermionic system is a Slater determinant, we can quantify the entanglement between the identical fermions by ...


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Necessary and sufficient condition for conjugacy: see Sylvester's law of inertia. In your notation, the two symmetric matrices $K$ and $K'$ are conjugate by a transformation $W^TKW = K'$ if and only if they have the same number of positive and negative eigenvalues (no null eigenvalues since both are nonsingular). The eigenvalues themselves need not be ...



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