Results 21 to 30 of about 244 (170)

A note on the three-way generalization of the Jordan canonical form

Open Mathematics, 2018
The limit point 𝓧 of an approximating rank-R sequence of a tensor Ƶ can be obtained by fitting a decomposition (S, T, U) ⋅ 𝓖 to Ƶ. The decomposition of the limit point 𝓧 = (S, T, U) ⋅ 𝓖 with 𝓖 = blockdiag(𝓖1, … , 𝓖m) can be seen as a three order ...
Cui Lu-Bin, Li Ming-Hui
doaj   +1 more source

Corrigendum to “Spectra universally realizable by doubly stochastic matrices”

Special Matrices, 2023
We correct an error in the statement and the proof of Theorem 2.1 and Corollary 2.1 in our previous study [Spec. Matrices 6 (2018), 301–309], Section 2: On nonnegative matrices similar to positive matrices.
Collao Macarena, Salas Mario, Soto Ricardo L.   +2 more
doaj   +1 more source

Pseudoinverse formulation of Rayleigh‐Schrödinger perturbation theory for the symmetric matrix eigenvalue problem

Journal of Applied Mathematics, Volume 2003, Issue 9, Page 459-485, 2003., 2003
A comprehensive treatment of Rayleigh‐Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore‐Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature.
Brian J. McCartin
wiley   +1 more source

The expected adjacency and modularity matrices in the degree corrected stochastic block model

Special Matrices, 2018
We provide explicit expressions for the eigenvalues and eigenvectors of matrices that can be written as the Hadamard product of a block partitioned matrix with constant blocks and a rank one matrix.
Fasino Dario, Tudisco Francesco
doaj   +1 more source

On the smallest singular value in the class of unit lower triangular matrices with entries in [−a, a]

Special Matrices, 2021
Given a real number a ≥ 1, let Kn(a) be the set of all n × n unit lower triangular matrices with each element in the interval [−a, a]. Denoting by λn(·) the smallest eigenvalue of a given matrix, let cn(a) = min {λ n(YYT) : Y ∈ Kn(a)}.
Altınışık Ercan
doaj   +1 more source

The nonexistence of rank 4 IP tensors in signature (1, 3)

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 5, Page 259-269, 2002., 2002
Let V be a real vector space of dimension 4 with a nondegenerate symmetric bilinear form of signature (1, 3). We show that there exists no algebraic curvature tensor R on V so that its associated skew‐symmetric operator R(⋅) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2‐planes in V.
Kelly Jeanne Pearson, Tan Zhang
wiley   +1 more source

The Diagonalizable Nonnegative Inverse Eigenvalue Problem

Special Matrices, 2018
In this articlewe provide some lists of real numberswhich can be realized as the spectra of nonnegative diagonalizable matrices but which are not the spectra of nonnegative symmetric matrices.
Cronin Anthony G, Laffey Thomas J.
doaj   +1 more source

Matrix splitting principles

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 5, Page 251-284, 2001., 2001
The systematic analysis of convergence conditions, used in comparison theorems proven for different matrix splittings, is presented. The central idea of this analysis is the scheme of condition implications derived from the properties of regular splittings of a monotone matrix A = M1 − N1 = M2 − N2.
Zbigniew I. Woźnicki
wiley   +1 more source

Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Special Matrices, 2019
The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix.
Marijuán C., Pisonero M., Soto Ricardo L.   +2 more
doaj   +1 more source

Fixed points of rotations of n‐sphere

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 221-222, 1999., 1999
We show that every rotation of an even‐dimensional sphere must have a fixed point.
Nagabhushana Prabhu
wiley   +1 more source