Results 321 to 330 of about 863,168 (361)
Some of the next articles are maybe not open access.
Spectra and Pseudospectra, 2020
. This paper is largely of expository nature. We generalize the determinantal and tracial inequalities, originating from Bloomfield-Watson and Knott, from the standpoint of majorization of eigenvalues, and observe the results as estimates of singular ...
F. Dufossé, B. Uçar
semanticscholar +1 more source
. This paper is largely of expository nature. We generalize the determinantal and tracial inequalities, originating from Bloomfield-Watson and Knott, from the standpoint of majorization of eigenvalues, and observe the results as estimates of singular ...
F. Dufossé, B. Uçar
semanticscholar +1 more source
DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
, 1967In this paper we study the distribution of eigenvalues for two sets of random Hermitian matrices and one set of random unitary matrices. The statement of the problem as well as its method of investigation go back originally to the work of Dyson [i] and I.
V. Marčenko, L. Pastur
semanticscholar +1 more source
On Eigenvalue Optimization [PDF]
SIAM Journal on Optimization, 1995 Summary: We study optimization problems involving eigenvalues of symmetric matrices. One of the difficulties with numerical analysis of such problems is that the eigenvalues, considered as functions of a symmetric matrix, are not differentiable at those points where they coalesce. We present a general framework for a smooth (differentiable) approach to
Alexander Shapiro, Michael K. H. Fan
openaire +1 more source
Combining eigenvalues and variation of eigenvectors for order determination
, 2016In applying statistical methods such as principal component analysis, canonical correlation analysis, and sufficient dimension reduction, we need to determine how many eigenvectors of a random matrix are important for estimation. This problem is known as
Wei Luo, Bing Li
semanticscholar +1 more source
On the higher eigenvalues for the $\infty$ -eigenvalue problem
Calculus of Variations and Partial Differential Equations, 2005The authors consider a nonlinear eigenvalue problem associated with a limiting version of the \(p\)-Laplacian for \(p=\infty\). Namely, if \(\Omega\) is an open subset of \(\mathbb R^n\), \(S_{n\times n}\) is the set of \(n\times n\) real symmetric matrices with real entries, the authors consider the nonlinear problem \( F_{\Lambda}(u,Du,D^2u)=0\) in \(
Peter Lindqvist, Petri Juutinen
openaire +2 more sources
Eigenvalues and condition numbers of random matrices
, 1988Given a random matrix, what condition number should be expected? This paper presents a proof that for real or complex $n \times n$ matrices with elements from a standard normal distribution, the ex...
A. Edelman
semanticscholar +1 more source
1986
Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed.
T. S. Blyth, Edmund F. Robertson
openaire +2 more sources
Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed.
T. S. Blyth, Edmund F. Robertson
openaire +2 more sources
On symplectic eigenvalues of positive definite matrices
, 2015If A is a 2n × 2n real positive definite matrix, then there exists a symplectic matrix M such that MTAM=DOOD where D = diag(d1(A), …, dn(A)) is a diagonal matrix with positive diagonal entries, which are called the symplectic eigenvalues of A.
R. Bhatia, Tanvi Jain
semanticscholar +1 more source