Author
S.W. Drury
Bio: S.W. Drury is an academic researcher from McGill University. The author has contributed to research in topics: Eigenvalues and eigenvectors & Singular value. The author has an hindex of 7, co-authored 34 publications receiving 235 citations.
Papers
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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.
Abstract: Let A = [ A11 A12 A21 A22 ] , where A22 is q× q , be an n× n complex matrix such that the numerical range of A is contained in Sα = {z ∈ C : Rz > 0, |Iz| (Rz) tanα} for some α ∈ [0,π/2) . We obtain the following singular value inequality: σ j(A/A11) sec2(α)σ j(A22), j = 1, . . . ,q, where A/A11 := A22−A21A−1 11 A12 and σ j(·) means the j -th largest singular value. This strengthens some recent results on determinantal inequalities. We also prove σ j(A) sec(α)λ j(RA), j = 1, . . . ,n, where λ j(·) denotes the j -th largest eigenvalue, complementing a result of Fan and Hoffman. Mathematics subject classification (2010): 15A45.
71 citations
TL;DR: 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.
51 citations
TL;DR: In this paper, a Fischer type determinantal inequality for matrices with given angular numerical range was obtained and the growth factor for Gaussian elimination for linear systems in which the coefficient matrix has this form was discussed.
19 citations
TL;DR: This work characterize the extremal digraphs which attain the maximum Perron root ofDigraphs with given arc connectivity and number of vertices given diameter and numberOf vertices.
13 citations
TL;DR: In this paper, the authors characterized the unique connected graphs whose distance spectral radius attains the maximum and minimum among all complements of trees, and determined the unique graphs whose least distance eigenvalues attains both the minimum and maximum distances among all trees.
13 citations
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01 Jan 1994
TL;DR: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element, so for any given data element or node in the list structure, the authors can talk in terms of a next element and a previous element.
Abstract: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element. Therefore, for any given data element or node in the list structure, we can talk in terms of a next element and a previous element.
381 citations
TL;DR: In this paper, the authors present families of Convex sets and characterizations of convex sets, as well as solutions, hints, and references for exercises for different types of sets.
Abstract: Fundamentals. Hyperplanes. Helly-Type Theorems. Kirchberger-Type Theorems. Special Topics in E2. Families of Convex Sets. Characterizations of Convex Sets. Polytopes. Duality. Optimization. Convex Functions. Solutions, Hints, and References for Exercises. Bibliography. Index.
287 citations
01 Jan 2009
151 citations
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.
Abstract: We show the uniqueness and construction (of the Z matrix in Theorem 2.1, to be exact) of a matrix decomposition and give an affirmative answer to a question proposed in [J. Math. Anal. Appl. 407 (2013) 436-442].
88 citations
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].
Abstract: Two new inequalities are proved for sector matrices. The first one complements a recent result in [Oper. Matrices, 8 (2014) 1143–1148]; the second one is an analogue of the AMGM inequality, where the geometric mean for two sector matrices was introduced in [Linear Multilinear Algebra 63 (2015) 296-301]. As an application of the second inequality, we present similar inequalities for singular values or norms. Mathematics subject classification (2010): 15A45, 15A42, 47A30.
62 citations