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2024 | OriginalPaper | Chapter

6. Schur Complement and Inequalities of Eigenvalues on Block Hadamard Product

Authors : Abdoulaye Mbaye, Etienne Mbaye

Published in: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Publisher: Springer Nature Switzerland

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Abstract

The Schur complement theory is very important in many areas such as statistics, matrix analysis, numerical analysis, and control theory. It is a powerful tool to discuss many significant results. In this chapter, we establish two inequalities on the eigenvalues of Schur complement of the block Hadamard product, deduce one important corollary, and illustrate them in numerical examples.

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previous chapter Computing Minimal Free Resolutions over Monomial Semirings with Coefficients in D-A Rings
next chapter A Perturbed Mann-Type Algorithm for Zeros of Maximal Monotone Mappings
Literature
1.
Mustafa Ozel and Ayca Ileri, Several Schur Complement inequalities on block Hadamard product, New Trends in Mathematical Sciences, 242–247(2017).
2.
M. Gunter, L, Klotz, Schur’s theorem for a block Hadamard product, Linear Algebra and its Application, 437(2012)948–956 .
3.
R.A. Horn, R. Mathias, Y. Nakamura, Inequalities for unitarily invariant norms and bilinear matrix products, Linear and Multilinear Algebra 30 (1991) 303–314.MathSciNetCrossRef
4.
F. Zhang (editor). The Schur Complement and its Applications. Numerical Methods and Algorithms, Springer-Verlag, New York, 2005.
Metadata
Title
Schur Complement and Inequalities of Eigenvalues on Block Hadamard Product
Authors
Abdoulaye Mbaye
Etienne Mbaye
Copyright Year
2024
Book
Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Print ISBN: 978-3-031-66221-8

Electronic ISBN: 978-3-031-66222-5

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-66222-5_6

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