Latent roots of lambda-matrices, Kronecker sums and matricial norms

José S. L. Vitória

Aplikace matematiky (1980)

  • Volume: 25, Issue: 6, page 395-399
  • ISSN: 0862-7940

Abstract

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Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for A where A is a latent root of a lambda-matrix. In particular, upper bounds for z are obtained where z is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for z .

How to cite

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Vitória, José S. L.. "Latent roots of lambda-matrices, Kronecker sums and matricial norms." Aplikace matematiky 25.6 (1980): 395-399. <http://eudml.org/doc/15165>.

@article{Vitória1980,
abstract = {Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for $\left|A\right|$ where $A$ is a latent root of a lambda-matrix. In particular, upper bounds for $\left|z\right|$ are obtained where $z$ is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for $\left|z\right|$.},
author = {Vitória, José S. L.},
journal = {Aplikace matematiky},
keywords = {Kronecker sum; latent roots; Kronecker sum; latent roots},
language = {eng},
number = {6},
pages = {395-399},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Latent roots of lambda-matrices, Kronecker sums and matricial norms},
url = {http://eudml.org/doc/15165},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Vitória, José S. L.
TI - Latent roots of lambda-matrices, Kronecker sums and matricial norms
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 6
SP - 395
EP - 399
AB - Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for $\left|A\right|$ where $A$ is a latent root of a lambda-matrix. In particular, upper bounds for $\left|z\right|$ are obtained where $z$ is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for $\left|z\right|$.
LA - eng
KW - Kronecker sum; latent roots; Kronecker sum; latent roots
UR - http://eudml.org/doc/15165
ER -

References

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  10. D. S. Mitrinovic, Analytic inequalities, Springer-Verlag, Berlin, 1970. (1970) Zbl0199.38101MR0274686
  11. M. Parodi, La localisation des valeurs caractéristiques des matrices et ses applications, Gauthier-Villars, Paris, 1969. (1969) 
  12. F. Robert, Normes vectorielles de vecteurs et de matrices, R.F.T.I. - CHIFFRES, 7, 4 (1964), 261-299. (1964) MR0205433
  13. F. Robert, Sur les normes vectorielles régulières sur un espace de dimension finie, C.R.A.S. Paris, 261 (1965), 5173-5176. (1965) MR0192317
  14. F. Robert, Matrices non-negatives et normes vectorielles, (Cours D.E.A.). Université Scientifique et Médicale, Lyon, 1973. (1973) 
  15. J. Vitória, Normas vectoriais de vectores e de matrizes, Report. Univ. Lourenço Marques (Mozambique), 1974. (1974) 
  16. J. Vitória, Matricial norms and lambda-matrices, Rev. Cienc. Mat. (Maputo, Mozambique), 5 (1974-75), 11-30. (1974) MR0457466
  17. J. Vitória, 10.1016/0024-3795(79)90139-3, Lin. Alg. its Appl. 28 (1979), 279-283. (1979) MR0549440DOI10.1016/0024-3795(79)90139-3

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