## Experimental Mathematics

- Experiment. Math.
- Volume 17, Issue 4 (2008), 499-510.

### Elimination for Coefficients of Special Characteristic Polynomials

W. Plesken and D. Robertz

#### Abstract

Computing the relations for the coefficients satisfied by the characteristic polynomial of the Kronecker product of a general $n \times n$ matrix by a general $m \times m$ matrix leads to an elimination problem that is already difficult for small values of $n$ and $m$. In this article we focus on the problems for $(n, m) \in \{ (2,3), (2,4), (3,3)$ and use these problems for developing and testing a new elimination technique called elimination by degree steering.

#### Article information

**Source**

Experiment. Math., Volume 17, Issue 4 (2008), 499-510.

**Dates**

First available in Project Euclid: 27 May 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1243429962

**Mathematical Reviews number (MathSciNet)**

MR2484433

**Zentralblatt MATH identifier**

1169.14324

**Subjects**

Primary: 14Q20: Effectivity, complexity 68W30: Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 20C40: Computational methods 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)

Secondary: 14A05: Relevant commutative algebra [See also 13-XX]

**Keywords**

Characteristic polynomial Kronecker product elimination Janet bases

#### Citation

Plesken, W.; Robertz, D. Elimination for Coefficients of Special Characteristic Polynomials. Experiment. Math. 17 (2008), no. 4, 499--510. https://projecteuclid.org/euclid.em/1243429962