Matrix Inequalities

Xingzhi Zhan (Autor)

Buch | Softcover

VIII, 124 Seiten

2002 | 2002
Springer Berlin (Verlag)
978-3-540-43798-7 (ISBN)

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The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.

Inequalities in the Loewner Partial Order: The Loewner-Heinz inequality; Maps on matrix spaces; Inequalities for matrix powers; Block matrix techniques.- Majorization and Eigenvalues: Majorizations; Eigenvalues of Hadamard products; Singular Values: Matrix Young inequalities; Singular values of Hadamard products; Differences of positive semidefinite matrices; Matrix Cartesian decompositions; Singular values and matrix entries.- Norm Inequalities: Operator monotone functions; Cartesian decompositions revisited; Arithmetic-geometric mean inequalities; Inequalities of Holder and Minkowski types; Permutations of matrix entries; The numerical radius; Norm estimates of banded matrices.- Solution of the van der Waerden Conjecture.

Erscheint lt. Verlag	9.7.2002
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 124 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	227 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	eigenvalue • Hadamard product • Inequalities • Matrix • matrix theory • Matrizen • Norms • Operator monotone functions • Permutation • Singular values
ISBN-10	3-540-43798-3 / 3540437983
ISBN-13	978-3-540-43798-7 / 9783540437987
Zustand	Neuware