# 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

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topJoão 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

top- [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. Zbl0576.15001
- [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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