Historical Introduction: Issai Schur and the Early Development of the Schur Complement.- Basic Properties of the Schur Complement.- Eigenvalue and Singular Value Inequalities of Schur Complements.- Block Matrix Techniques.- Closure Properties.- Schur Complements and Matrix Inequalities: Operator-Theoretic Approach.- Schur complements in statistics and probability.- Schur Complements and Applications in Numerical Analysis.
From the reviews of the first edition: "The book consists of eight chapters, each written by experts in their field, devoted to certain aspects and applications of the Schur complement. They can be read independently of each other. ... The book can serve as a research reference, as it contains many new results and results not yet appeared in books. The articles contain thorough expositions, so they can be understood by anyone having a good knowledge of linear algebra." (Ludwig Elsner, Zentralblatt MATH, Vol. 1075, 2006)
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