We give an estimate for the relative change in the eigenvalues, as well as bounds on the angles between the perturbed and unperturbed eigenvectors. This class includes componentwise, or more generally 'localized', relative perturbations of Laplacians. We show that the estimate is optimal up to ...
Reinhard Nabben.A note on comparison theorems for splittings and multisplittings of Hermitian positive definite matrices. Linear Algebra and Its Applications . 1996A note on comparison theorems for splittings and multisplittings of Hermitian positive definite matrices - Nabben - 1996 () Citation ...
A note on the growth factor in Gaussian elimination for generalized Higham matricesMathematics - Numerical Analysis65F1065F1565F50The Higham matrix is a complex symmetric matrix A=B+iC, where both B and Care real, symmetric and positive definite and $\\mathrm{i}=\\sqrt{-1}$ is theimaginary...
Let the columns of the matrices X and Y be the right and the left eigenvectors of (1) respectively. We can write (2)BXΛ−AX=0,ΛY∗B−Y∗A=0,(3)B˜X˜Λ˜−A˜X˜=0,Λ˜Y˜∗B˜−Y˜∗A˜=0. Note, that the regularity assumption implies that ...
LetAandBbe positive semidefinite matrices of the same size. Using a trace inequality of Ando, Hiai, and Okubo, we prove that ‖B1−tA2t−1B1−t+A1−tB2t−1A1−t‖2≤‖A+B‖2 fort∈[12,34], where‖.‖2denotes the Hilbert-Schmidt norm. This gives an affimative answer to...
Note that although we have concentrated on going from one interval to the next on the left, the results above may also be used in reverse fashion to obtain the next adjacent interval to the right. 5. v(n O) AS A FUNCTION OF C Letting Ii 0 (C) be the solution to the problem of ...
(note that we use m instead of w in [ 20 ] for the size of the blocks). the 2-point correlation function can be expressed in terms of a superintegral of a superfunction \(f(\{\breve{\mathcal {s}}_i\}_{i=1}^w)\) with a collection of \(4\times 4\) supermatrices \(\...
There is also a lower bound on this quantity by the set of separable states, however, it is generally depending on the dimension and on the choice of the set MUBs52. Note, that in particular to detect bound entangled states a reordering of the basis of one subsystem is needed else the...
We consider the nonlinear matrix equation (1.1)where is a positive integer, is an nonsingular matrix, is a positive semidefinite matrix and is a positive definite matrix. We denote by the geometric mean of positive definite matrices and , which is extended by Ando [1] from the case of two...
On the other hand, m(r;K′−u1)=0 (since m(r;K′)=1, as already proved above, and since u1 is a downer in K′). This completes the proof. □ Remark 4.1 First, note that vertices in U may, or may not be adjacent. However, this fact does not influence the conclusion ...