Results 41 to 50 of about 5,647,728 (213)
有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)
Zhejiang Daxue xuebao. Lixue ban, 2019 In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成) +1 more
doaj +1 more source
A Characterization on Singular Value Inequalities of Matrices
Journal of Function Spaces, 2020 We obtain a characterization of pair matrices A and B of order n such that sjA≤sjB, j=1, …, n, where sjX denotes the j-th largest singular values of X. It can imply not only some well-known singular value inequalities for sums and direct sums of matrices
Wei Dai, Yongsheng Ye
doaj +1 more source
A class of positive semidefinite matrices
Linear Algebra and its Applications, 1987 It is a known fact that, given a positive definite matrix \(y_{ij}\), the ``standardized'' matrix \(y_{ij}(y_{ii}y_{jj})^{-}\) is again positive definite. The authors investigate more general standardization methods of the form \(a_{ij}(\alpha)y_{ij}\) where \(\alpha\) is a positive number and \(a_{ij}(\alpha)=(\phi (x_ i,\alpha)+\phi (x_ j,\alpha))^{-}
Russell, A.M., Upton, C.J.F.
openaire +2 more sources
Measuring Sphericity in Positive Semi-Definite Matrices
AxiomsThe measure of sphericity for positive semi-definite matrices plays a crucial role in understanding their geometric properties, especially in high-dimensional settings.
Dário Ferreira, Sandra S. Ferreira
doaj +1 more source
Using distance on the Riemannian manifold to compare representations in brain and in models
NeuroImage, 2021 Representational similarity analysis (RSA) summarizes activity patterns for a set of experimental conditions into a matrix composed of pairwise comparisons between activity patterns.
Mahdiyar Shahbazi +3 more
doaj +1 more source
Hyperbolic Relaxation of $k$-Locally Positive Semidefinite Matrices
SIAM Journal on Optimization, 2022 A successful computational approach for solving large-scale positive semidefinite (PSD) programs is to enforce PSD-ness on only a collection of submatrices. For our study, we let $\mathcal{S}^{n,k}$ be the convex cone of $n\times n$ symmetric matrices where all $k\times k$ principal submatrices are PSD. We call a matrix in this $k$- locally PSD.
Grigoriy Blekherman +3 more
openaire +3 more sources
Trace-Inequalities and Matrix-Convex Functions
Fixed Point Theory and Applications, 2010 A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X↦f(X) via functional calculus from the convex set of n×n Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of
Tsuyoshi Ando
doaj +2 more sources
On the cone of positive semidefinite matrices
Linear Algebra and its Applications, 1987 An as yet unsolved problem in matrix theory is to classify those linear transformations of the \(n\times n\) complex matrices which leave the cone, PSD, of positive semidefinite Hermitian matrices invariant. The present note surveys the known results on the structure of the cone PSD, and some of the results concerning linear transformations which map ...
Hill, Richard D., Waters, Steven R.
openaire +2 more sources
Advanced Intelligent Systems, EarlyView.A scalable distributed observer framework for LiDAR sensor networks is presented for robust tracking and pose estimation of mobile robots. By combining adaptable 3D detection, clustering‐based communication reduction, and intermittent inertial fusion, accurate and efficient estimation is achieved under occlusions and sensing constraints, with formally ...
Isabella Luppi, Ehsan Hashemi
wiley +1 more source
Laser &Photonics Reviews, EarlyView.Coherence variation is ubiquitous in nature, yet determining how it constrains physical observables remains challenging for multimode waves. To address this challenge, this work establishes a majorization‐based theory that identifies the supremum and infimum in the set of input coherence spectra, which provide optimal universal bounds for any linear ...
Shiyu Li, Cheng Guo
wiley +1 more source