##  [Schur Complement](/schur-complement) 

  ##  [Schur Complement](https://natural.quantumdictionary.io/schur-complement-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Given a block matrix M = [[A, B],[C, D]] with A invertible, the Schur complement of A in M is S = D − C A^{-1} B; it reduces block elimination and expresses determinants and inverses via block formulas.