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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.
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