Determinants of block matrices with noncommuting blocks

@article{Sothanaphan2017DeterminantsOB,
  title={Determinants of block matrices with noncommuting blocks},
  author={Nat Sothanaphan},
  journal={Linear Algebra and its Applications},
  year={2017},
  volume={512},
  pages={202-218}
}
  • Nat Sothanaphan
  • Published 2017
  • Mathematics
  • Linear Algebra and its Applications
Abstract Let M be an m n × m n matrix over a commutative ring R. Divide M into m × m blocks. Assume that the blocks commute pairwise. Consider the following two procedures: (1) Evaluate the n × n determinant formula at these blocks to obtain an m × m matrix, and take the determinant again to obtain an element of R; (2) Take the m n × m n determinant of M. It is known that the two procedures give the same element of R. We prove that if only certain pairs of blocks of M commute, then the two… Expand

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