#### Title

### 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