Nearly positive matrices

Nearly positive matrices

Nearly positive matrices are nonnegative matrices which, when premultiplied by orthogonal matrices as close to the identity as one wishes, become positive. In other words, all columns of a nearly positive matrix are mapped simultaneously to the interior of the nonnegative cone by mutiplication by a sequence of orthogonal matrices converging to the identity. In this paper, nearly positive matric...

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

Block Diagonalization of Nearly Diagonal Matrices

In this paper we study the effect of block diagonalization of a nearly diagonal matrix by iterating the related Riccati equations. We show that the iteration is fast, if a matrix is diagonally dominant or scaled diagonally dominant and the block partition follows an appropriately defined spectral gap. We also show that both kinds of diagonal dominance are not destroyed after the block diagonali...

r-Indecomposable and r-Nearly Decomposable Matrices

Let n, r be integers with 0 ≤ r ≤ n− 1. An n×n matrix A is called r-partly decomposable if it contains a k×l zero submatrix with k+l = n−r+1. A matrix which is not r-partly decomposable is called r-indecomposable (shortly, r-inde). Let Eij be the n × n matrix with a 1 in the (i, j) position and 0’s elsewhere. If A is r-indecomposable and, for each aij 6= 0, the matrix ∗Research supported by Nat...

Eigensolutions of perturbed nearly defective matrices