Hermitian Pencils With A Cubic Minimal Polynomial
Document Type
Article
Publication Date
12-1-1982
Published In
Linear Algebra And Its Applications
Abstract
Let A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices. We show that if the minimal polynomial of the pencil xH + yK has degree 3, then there is a unitary matrix U such that U⁻¹AU is block diagonal with blocks of size 3 × 3 or smaller. This is a special case of a conjecture made by Kippenhahn in 1951.
Recommended Citation
Helene Shapiro.
(1982).
"Hermitian Pencils With A Cubic Minimal Polynomial".
Linear Algebra And Its Applications.
Volume 48,
81-103.
DOI: 10.1016/0024-3795(82)90100-8
https://works.swarthmore.edu/fac-math-stat/226