Calculating Determinants of Block Matrices
  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 allows one to reduce the determinant of a matrix with N^2 blocks to the product of the determinants of N distinct combinations of single blocks. This procedure proves useful in the analytic description of physical systems with multiple discrete variables, as it provides a systematic method for evaluating determinants which might otherwise be analytically intractable. 
Philip D. Powell
math.RA math.NA