## 14 Citations

Interlacing properties of the eigenvalues of some matrix classes

- Mathematics
- 2012

Theorems and counterexamples on structured matrices

- Mathematics
- 2005

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.…

Interlacing Inequalities for Totally Nonnegative

- Mathematics
- 2000

Suppose 1 n 0 are the eigenvalues of an n n totally nonnegative matrix, and ~ 1 ~ k are the eigenvalues of a k k principal submatrix. A short proof is given of the interlacing inequalities: j are…

Eigenvalues of products of matrices and submatrices in certain positivity classes

- Mathematics
- 2000

If A and B are n-by-n, positive semidefinite Herimitian matrices, then for any φ≠α⊆{1,2,… n}. A certain converse is given, as well as analogs for the product of several m-matrices and totally…

An inverse eigenvalue problem for totally nonnegative matrices

- Mathematics
- 1985

In a previous paper we proved that the diagonal elements of a totally nonnegative matrix are majorized by its eigenvalues. In this note we show that the majorization of a vector of nonnegative real…

An Interlacing Property of Eigenvalues ofStrictly Totally Positive

- Mathematics
- 1998

We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive matrices. x1. Introduction The central results concerning eigenvalues and eigenvectors…

Spectral Structures of Irreducible Totally Nonnegative Matrices

- MathematicsSIAM J. Matrix Anal. Appl.
- 2000

This work defines a notion of "principal rank" and employs this idea throughout to characterize all possible Jordan canonical forms (Jordan structures) of irreducible totally nonnegative matrices of n-by-n matrices.

## References

SHOWING 1-7 OF 7 REFERENCES

An inverse eigenvalue problem for totally nonnegative matrices

- Mathematics
- 1985

In a previous paper we proved that the diagonal elements of a totally nonnegative matrix are majorized by its eigenvalues. In this note we show that the majorization of a vector of nonnegative real…

Extremal eigenvalue problems for convex sets of symmetric matrices and operators

- Mathematics
- 1973

LetA1,...,An andK bem×m symmetric matrices withK positive definite. Denote byC the convex hull of {A1,...An}. Let {λp(KA)}1n be then real eigenvalues ofKA arranged in decreasing order. We show that…

Oscillation Properties of Generalized Characteristic Polynomials for Totally Positive and Positive Definite Matrices

- Mathematics
- 1974

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

- Mathematics, Philosophy
- 1976

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…