ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 15, 41 Möller, Herbert, University of Münster, Germany New central algorithms in linear algebra In the textbook of the reference all suitable results of linear algebra are derived in algorithmic form. Besides the book contains six new central algorithms about generalized inverses, canonical forms of equivalent and similar matrices, spectral decomposition, testing of diagonalizability not using eigenvalues and efficient surefire approximation of all polynomial roots. The last three of these algorithms will be presented. The diagonalizability criterion can be stated here: The square matrix A with decomposable characteristic polynomial p(t) = det(tI − A) is diagonalizable iff the adjoint of tI − A as a polynomial in t with matrix coefficients is divisible by the polynomial gcd(p(t), p′(t)). Reference: H. Möller, Algorithmische Lineare Algebra. Verlag Vieweg, Wiesbaden 1997.