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Efficient calculation of Slater determinants

Let the current position in phase space be represented by the (Nd)-element vector rold and the new suggested position by the vector rnew.

The inverse of ˆD can be expressed in terms of its cofactors Cij and its determinant (this our notation for a determinant) |ˆD|:

d1ij=Cji|ˆD|

Notice that the interchanged indices indicate that the matrix of cofactors is to be transposed.