# Fiedler Companion Linearizations and the Recovery of Minimal Indices

@article{Tern2010FiedlerCL,
title={Fiedler Companion Linearizations and the Recovery of Minimal Indices},
author={F. Ter{\'a}n and F. Dopico and D. S. Mackey},
journal={SIAM J. Matrix Anal. Appl.},
year={2010},
volume={31},
pages={2181-2204}
}
• Published 2010
• Computer Science, Mathematics
• SIAM J. Matrix Anal. Appl.
A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalent matrix pencil—a process known as linearization. For any regular matrix polynomial, a new family of linearizations generalizing the classical first and second Frobenius companion forms has recently been introduced by Antoniou and Vologiannidis, extending some linearizations previously defined by Fiedler for scalar polynomials. We prove that these pencils are linearizations even when \$P(\lambda… Expand
94 Citations

#### References

SHOWING 1-10 OF 43 REFERENCES
Symmetric Linearizations for Matrix Polynomials
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 2006
• 125
• PDF
The Conditioning of Linearizations of Matrix Polynomials
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 2006
• 120
• PDF
Vector Spaces of Linearizations for Matrix Polynomials
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 2006
• 292
• PDF
Definite Matrix Polynomials and their Linearization by Definite Pencils
• Computer Science, Mathematics
• SIAM J. Matrix Anal. Appl.
• 2009
• 35
• PDF