• Corpus ID: 10340027

Theorems and counterexamples on structured matrices

  title={Theorems and counterexamples on structured matrices},
  author={O. Holtz},
  journal={arXiv: Rings and Algebras},
  • O. Holtz
  • Published 27 December 2005
  • Mathematics
  • arXiv: Rings and Algebras
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz, Hessenberg, Hankel, Cauchy, and other) are used extensively throughout the thesis. 

Figures from this paper


On some conjectures on the spectra of τ-matrices
We will consider three conjectures of Schneider and Varga concerning the location of eigenvalues of ω- and τ-matices in the complex plane, and extend the known results to n ⩽ 4. We will further show
Nonnegative Matrices in the Mathematical Sciences
1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of nonnegative matrices 4. Symmetric nonnegative matrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative
Notes on ω- and τ-matrices
Constructive Approximation
This paper works on [-1, 1 ] and obtains Markov-type estimates for the derivatives of polynomials from a rather wide family of classes of constrained polynomes and results turn out to be sharp.
Inverses of Band Matrices and Local Convergence of Spline Projections
It is shown that the size of the entries in the inverse of a band matrix can be bounded in terms of the norm of the matrix, the norm of its inverse and the bandwidth. In many cases this implies that
A research problem
We present a conjecture which when true would generalize T. Ando's characterization of the numerical radius of (bounded linear) operators on a Hilbert space (see [A]). Some evidence for the validity
On complex eigenvalues ofM andP matrices
SummaryInequalities are obtained for the complex eigenvalues of anM matrix or aP matrix which depend only on the order of the matrix.
Weak interlacing properties of totally positive matrices