Not all GKK τ-matrices are stable

@article{Holtz1999NotAG,
  title={Not all GKK $\tau$-matrices are stable},
  author={Olga Holtz},
  journal={Linear Algebra and its Applications},
  year={1999},
  volume={291},
  pages={235-244}
}
  • Olga Holtz
  • Published 15 April 1999
  • Mathematics
  • Linear Algebra and its Applications

G-varieties and the principal minors of symmetric matrices

G-Varieties and the Principal Minors of Symmetric Matrices. (May 2009) Luke Aaron Oeding, B.A., Franklin & Marshall College Chair of Advisory Committee: Dr. J.M. Landsberg The variety of principal

SPECTRAL PROPERTIES OF SIGN SYMMETRIC MATRICES

Spectral properties of sign symmetric matrices are studied.A criterion for sign symmetry of shifted basic circulant permutation matrices is proven, and is then used to answer the question which

A Bibliography of Publications in Linear Algebra and its Applications: 1980{1989

(AB) = B− mrA − lr [WHG79]. (k) [Cha79]. (k, n) [MT79]. 0 [JGK79]. 0− 1 [HP78]. 2 [Sto79]. 2× 2 [Est79]. 3× 3 [AYP79]. A [Nic79]. AB +BA [Nic79]. AX − Y B = C [BK79a]. AX = B [PM79]. AXC = B [PM79].

Set-theoretic defining equations of the variety of principal minors of symmetric matrices

The variety of principal minors of $n\times n$ symmetric matrices, denoted $Z_{n}$, is invariant under the action of a group $G\subset \GL(2^{n})$ isomorphic to $\G$. We describe an irreducible

Theorems and counterexamples on structured matrices

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.

in Linear Algebra and its Applications : 1990 – 1999

(J.J ′) [?]. (λ,G) [?]. (p, q) [?]. ( AB C0) [?]. (u, i) [?]. ∗ [?, ?]. −1− 2 [?]. 0 [?]. {0, 12 , 1} [?]. 0,±1 [?]. 1 [?, ?, ?, ?]. 2 [?, ?, ?, ?, ?, ?, ?]. 2K [?]. 2× 2 [?, ?, ?, ?, ?, ?]. 3 [?].

R A ] 5 S ep 2 00 1 Open problems on GKK τ-matrices

TLDR
Several open problems on GKK τ -matrices raised by examples showing that some such matrices are unstable are proposed.

A pr 2 00 6 Hyperdeterminantal relations among symmetric principal minors

The principal minors of a symmetric n×n-matrix form a vector of length 2n. We characterize these vectors in terms of algebraic equations derived from the 2×2×2-hyperdeterminant.

References

SHOWING 1-9 OF 9 REFERENCES

The Hadamard-Fischer inequality for a class of matrices defined by eigenvalue monotonicity

1) Spec A[Jl.l n IR =1= t/>, for t/> c Jl. S (n), 2) I(A[J-L]) « I(A[v]), if t/> c v S Jl. S (n), where I(A[Jl.]) = min(Spec A[Jl.l n IR). For A, BE W(n), define A «, B by I(A[J-L]) « I(B[J-L]), for

A class of positive stable matrices

The characteristic roots of this matrix are, approximately , 6_85 and 2_58 ± O_28i_ It is perhaps ~f interest, however , that ~ll positiye sign-symmetric matrices are positive stable, i_ eo, all

Recent directions in matrix stability

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

Oscillation matrices and kernels and small vibrations of mechanical systems

Introduction Review of matrices and quadratic forms Oscillatory matrices Small oscillations of mechanical systems with $n$ degrees of freedom Small oscillations of mechanical systems with an infinite

Recent results in linear algebra and its applications (in Russian)

  • in: Numerical Methods in Linear Algebra, Proceedings of the Third Seminar of Numerical Applied Mathematics, Akad. Nauk SSSR Sibirsk. Otdel. Vychisl. Tsentr, Novosibirsk
  • 1978

Recent results in linear algebra and its applications (in Russian), in: Numerical Methods in Linear Algebra

  • Proceedings of the Third Seminar of Numerical Applied Mathematics, Akad. Nauk SSSR Sibirsk. Otdel. Vychisl. Tsentr
  • 1978