Review
Version 1
Preserved in Portico This version is not peer-reviewed
On the Minimum Polynomial and Applications
Version 1
: Received: 20 December 2021 / Approved: 21 December 2021 / Online: 21 December 2021 (12:38:45 CET)
How to cite: Halidias, N. On the Minimum Polynomial and Applications. Preprints 2021, 2021120329. https://doi.org/10.20944/preprints202112.0329.v1 Halidias, N. On the Minimum Polynomial and Applications. Preprints 2021, 2021120329. https://doi.org/10.20944/preprints202112.0329.v1
Abstract
In this note we study the computation of the minimum polynomial of a matrix $A$ and how we can use it for the computation of the matrix $A^n$. We also describe the form of the elements of the matrix $A^{-n}$ and we will see that it is closely related with the computation of the Drazin generalized inverse of $A$. Next we study the computation of the exponential matrix and finally we give a simple proof of the Leverrier - Faddeev algorithm for the computation of the characteristic polynomial.
Keywords
Minimum polynomial; characteristic polynomial; exponential matrix; Drazin inverse; Leverrier - Faddeev algorithm
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
