#### Document Type

Article

#### Publication Date

6-2010

#### Publication Title

Alexandria Journal of Mathematics

#### ISSN

2090‐4789

#### Abstract

Linear matrix pencil, denoted by (* A,B*), plays an important role in control systems and numerical linear algebra. The problem of finding the eigenvalues of (A,B) is often solved numerically by using the well-known QZ method. Another approach for exploring the eigenvalues of (

*) is by way of its characteristic polynomial,*

**A,B***P*(λ)=

*A*− λ

*B*. There are other applications of working directly with the characteristic polynomial, for instance, using Routh-Hurwitz analysis to count the stable roots of

*P*(λ) and transfer function representation of control systems governed by differential-algebraic equations. In this paper, we present an algorithm for algebraic construction of the characteristic polynomial of a regular linear pencil. The main theorem reveals a connection between the coefficients of

*P*(λ) and a lexicographic combination of the rows between matrices

*and*

**A***.*

**B**#### Recommended Citation

Wu, Yan, Phillip Lorren.
2010.
"On the Characteristic Polynomial of Regular Linear Matrix Pencil."
*Alexandria Journal of Mathematics*, 1 (1): 53-60.
source: https://alexjournals.org/public/AlexJournal/Mathematics/volume/1/1/June%202010

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/236

## Comments

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