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This paper presents a method for expressing the determinant of an N {\times}N complex block matrix in terms of its constituent blocks. The result allowsone to reduce the determinant of a matrix with N^2 blocks to the product of thedeterminants of N distinct combinations of single blocks. This procedure provesuseful in the analytic description of physical systems with multiple discretevariables, as it provides a systematic method for evaluating determinants whichmight otherwise be analytically intractable.

Calculating Determinants of Block Matrices