On the matrix form of Kronecker lemma

João Lita da Silva; António Manuel Oliveira

Discussiones Mathematicae Probability and Statistics (2009)

  • Volume: 29, Issue: 2, page 233-243
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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João Lita da Silva, and António Manuel Oliveira. "On the matrix form of Kronecker lemma." Discussiones Mathematicae Probability and Statistics 29.2 (2009): 233-243. <http://eudml.org/doc/277054>.

@article{JoãoLitadaSilva2009,
abstract = {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.},
author = {João Lita da Silva, António Manuel Oliveira},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {matrix Kronecker lemma; matrix analysis; convergence},
language = {eng},
number = {2},
pages = {233-243},
title = {On the matrix form of Kronecker lemma},
url = {http://eudml.org/doc/277054},
volume = {29},
year = {2009},
}

TY - JOUR
AU - João Lita da Silva
AU - António Manuel Oliveira
TI - On the matrix form of Kronecker lemma
JO - Discussiones Mathematicae Probability and Statistics
PY - 2009
VL - 29
IS - 2
SP - 233
EP - 243
AB - 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.
LA - eng
KW - matrix Kronecker lemma; matrix analysis; convergence
UR - http://eudml.org/doc/277054
ER -

References

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  1. [1] B.D.O. Anderson and J.B. Moore, A Matrix Kronecker Lemma, Linear Algebra Appl. 15 (1976), 227-234. 
  2. [2] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer 1997. 
  3. [3] R.A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press 1985. Zbl0576.15001
  4. [4] B M. Makarov, M.G. Goluzina, A.A. Lodkin and A.N. Podkorytov, Selected Problems in Real Analysis, American Mathematical Society 1992. 

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