On the matrix form of Kronecker lemma

• Autorzy: João Lita da Silva , António Manuel Oliveira
• Języki publikacji: EN

Abstrakty

EN

A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.

Słowa kluczowe

EN

matrix Kronecker lemma; matrix analysis; convergence

Kategorie tematyczne

• 15A23: Factorization of matrices
• 15A09: Matrix inversion, generalized inverses
• 40A05: Convergence and divergence of series and sequences

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 233-243

Daty

wydano

2009

otrzymano

2009-09-06

Twórcy

autor

João Lita da Silva

• Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

autor

António Manuel Oliveira

• Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

Bibliografia

• [1] B.D.O. Anderson and J.B. Moore, A Matrix Kronecker Lemma, Linear Algebra Appl. 15 (1976), 227-234.
• [2] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer 1997.
• [3] R.A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press 1985.
• [4] B M. Makarov, M.G. Goluzina, A.A. Lodkin and A.N. Podkorytov, Selected Problems in Real Analysis, American Mathematical Society 1992.

Identyfikatory

DOI

10.7151/dmps.1117