Name
Title | ||
|---|---|---|
Crouzeix's Conjecture Holds for Tridiagonal 3 x 3 Matrices with Elliptic Numerical Range Centered at an Eigenvalue. |
Abstract | ||
|---|---|---|
Crouzeix stated the following conjecture in [Integral Equations Operator Theory, 48 (2004), pp. 461-477]: For every n x n matrix A and every polynomial p, parallel to p(A)parallel to <= 2 max(z is an element of)W(A)vertical bar p(z)vertical bar, where W(A) is the numerical range of A. We show that the conjecture holds in its strong, completely bounded form, i.e., where p above is allowed to be any matrix-valued polynomial, for all tridiagonal 3 x 3 matrices with constant main diagonal, [GRAPHICS] , a, b(k), c(k) is an element of C, or equivalently, for all complex 3 x 3 matrices with elliptic numerical range and one eigenvalue at the center of the ellipse. We also extend the main result of Choi in [Linear Algebra Appl., 438 (2013), pp. 3247-3257] slightly. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1110663 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
Crouzeix's conjecture,3 x 3 matrix,elliptic numerical range | Tridiagonal matrix,Discrete mathematics,Polynomial,Matrix (mathematics),Mathematical analysis,Numerical range,Operator theory,Mathematics,Eigenvalues and eigenvectors,Bounded function,Main diagonal | Journal |
Volume | Issue | ISSN |
39 | 1 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christer Glader | 1 | 1 | 1.30 |
| Mikael Kurula | 2 | 1 | 1.71 |
| Mikael Lindström | 3 | 1 | 0.96 |