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Calculating Determinants of Block Matrices

2011/12/16 by Philip D. Powell, Powell, Philip D.
Chemistry · Computer Science · Physics and Astronomy · #15A15 (Primary) 15A09 (Secondary) #Advanced Physical and Chemical Molecular Interactions #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Rings and Algebras (math.RA) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.1112.4379

openalex publication_date 2011/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a method for expressing the determinant of an N × N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N2 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.

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