On the Computation of the Minimum Polynomial and Applications
Asian Research Journal of Mathematics,
Aims/Objectives: In this review article we study the computation of the minimum polynomial
of a matrix A and how we can use it for the computation of the matrix An. 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 nally we give a simple proof of the Leverrier - Faddeev algorithm for
the computation of the characteristic polynomial.
- Minimum polynomial
- characteristic polynomial
- exponential matrix
- Drazin inverse
- Leverrier - Faddeev algorithm
How to Cite
Academy Sciences. 2008;56.
Higham N. Functions of matrices, theory and computation. SIAM; 2008.
Israel A, Grevill T. Genelalized inverses, theory and applications. Springer; 2003.
Shui-Hung Hou. A simple proof of the Leverrier - Faddeev characteristic polynomial algorithm.
SIAM REV. 1998;40(3):706-709.
Brand L. The companion matrix and its Properties. The American Mathematical Monthly.
Berberian S. Linear Algebra, Oxford Science Publications; 1992.
Davis P. Interpolation and approximation. Dover; 1975.
Larson R, Falvo D. Elementary linear algebra. Houghton Miin Harcourt Publishing Company;
Lipschutz S, Lipson M. Linear algebra. McGraw Hill; 2009.
Moler C, Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty
- ve years later. SIAM Review; 2003.
Penrose R. A Generalized Inverse for matrices., Mathematical Proceedings of the Cambridge
Philosophical Society. 1955;406-413:51.
Ricardo H. A Modern Introduction to Linear Algebra. CRC Press; 2010.
Silvester JR. Determinants of block Matrices. Math. Gaz. 2000;84(501):460-467.
Shoup V. Ecient Computation of Minimal Polynomials in Algebraic Extensions of Finite
Flowe R, Harris G. A note on genelalized Vandermonde determinants. SIAM J. Matrix Anal.
Cambell S, Meyer C. Generelized Inverses of Linear Trasformations. SIAM; 2009.
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