Chapter 12
Schur Complements
Roger A. Horn
The University of Utah
Fuzhen Zhang
Nova Southeastern University
The Schur complement, named after Issai Schur (1875-1941), plays an important role as a basic tool in mathematical research and applications, particularly in matrix analysis, statistics, and numerical analysis. It was named and given a notation in 1968 by Emilie Haynsworth (1916-1985). The idea of using the Schur complement technique to deal with linear systems and matrix problems is classical. It was certainly known to James Joseph Sylvester (1814-1897) in 1851 [Syl52], and probably also to Carl Friedrich Gauss (1777-1855) (for Gaussian elimination). A fundamental determinant identity presented by Schur in 1917 [Sch17] was referred to ...
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