Journal ArticleDOI
Principal powers of matrices with positive definite real part
TLDR
In this paper, the principal powers of complex square matrices with positive definite real part were studied and the notion of geometric mean was extended to such matrices and an operator norm bound was established.Abstract:
We study principal powers of complex square matrices with positive definite real part, or with numerical range contained in a sector. We extend the notion of geometric mean to such matrices and we establish an operator norm bound in this context.read more
Citations
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Journal ArticleDOI
A matrix decomposition and its applications
TL;DR: In this paper, the uniqueness and construction of the Z matrix in Theorem 2.1 was shown and an affirmative answer to a question proposed in [J. Math. Anal. Appl. 407 (2013) 436-442 was given.
Journal ArticleDOI
Some inequalities for sector matrices
TL;DR: In this paper, two new inequalities for sector matrices are proved for singular values or norms, which complements a recent result in [Oper. Matrices, 8 (2014) 1143-1148] and [Linear Multilinear Algebra 63 (2015) 296-301].
Journal ArticleDOI
Relative entropy and Tsallis entropy of two accretive operators
TL;DR: In this article, the weighted geometric mean and Tsallis entropy of positive invertible operators are defined. But the present definitions and their related results extend those already introduced in the literature for positive inverse operators.
Journal ArticleDOI
A property of the geometric mean of accretive operators
Minghua Lin,Fangfang Sun +1 more
TL;DR: In this paper, an inequality for the geometric mean of accretive operators was proved, using the result of Mathias and Drury [SIAM J. Matrix Anal. Appl. 2015;63:296-301].
Journal ArticleDOI
Numerical radii of accretive matrices
TL;DR: The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis as discussed by the authors, and due to the difficulty in computing the numerical radius, inequalities bounding it h...
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Tables of Integrals, Series, and Products
Book
Positive Definite Matrices
TL;DR: In this paper, the authors present a synthesis of the considerable body of new research into positive definite matrices, which have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory and geometry.
Journal ArticleDOI
Singular value inequalities for matrices with numerical ranges in a sector
S.W. Drury,Minghua Lin +1 more
TL;DR: In this paper, the authors obtained the following singular value inequality: σ j(A/A11) sec2(α)σ j (A22), j = 1,...,q, where j(·) denotes the j -th largest eigenvalue.