| Title:
|
Latent roots of lambda-matrices, Kronecker sums and matricial norms (English) |
| Author:
|
Vitória, José |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
25 |
| Issue:
|
6 |
| Year:
|
1980 |
| Pages:
|
395-399 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\left|z\right|$. (English) |
| Keyword:
|
Kronecker sum |
| Keyword:
|
latent roots |
| MSC:
|
15A42 |
| MSC:
|
15A45 |
| MSC:
|
30C15 |
| idZBL:
|
Zbl 0469.15005 |
| idMR:
|
MR0596845 |
| DOI:
|
10.21136/AM.1980.103877 |
| . |
| Date available:
|
2008-05-20T18:15:22Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103877 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] J. E. Dennis (JR) J. F. Traub R. P. Weber: On the matrix polynomial, lambda-matrix and eigenvalue problems.Technical Report 71 - 109, Depart. Computer Science, Cornell Univ. 1971. |
| Reference:
|
[4] E. Deutsch: Matricial norms.Numer. Math. 16 (1970), 73 - 84. Zbl 0206.35801, MR 0277552, 10.1007/BF02162408 |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[8] P. Lancaster: Theory of Matrices.Academic Press, New York, 1969. Zbl 0186.05301, MR 0245579 |
| Reference:
|
[9] M. Marden: Geometry of polyomials.American Mathematical Society, Providence, Rhode Island, 2nd. edition, (Math. Survey n° 3), 1966. MR 0225972 |
| Reference:
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[10] D. S. Mitrinovic: Analytic inequalities.Springer-Verlag, Berlin, 1970. Zbl 0199.38101, MR 0274686 |
| Reference:
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| Reference:
|
[12] F. Robert: Normes vectorielles de vecteurs et de matrices.R.F.T.I. - CHIFFRES, 7, 4 (1964), 261-299. MR 0205433 |
| Reference:
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[13] F. Robert: Sur les normes vectorielles régulières sur un espace de dimension finie.C.R.A.S. Paris, 261 (1965), 5173-5176. MR 0192317 |
| Reference:
|
[14] F. Robert: Matrices non-negatives et normes vectorielles.(Cours D.E.A.). Université Scientifique et Médicale, Lyon, 1973. |
| Reference:
|
[15] J. Vitória: Normas vectoriais de vectores e de matrizes.Report. Univ. Lourenço Marques (Mozambique), 1974. |
| Reference:
|
[16] J. Vitória: Matricial norms and lambda-matrices.Rev. Cienc. Mat. (Maputo, Mozambique), 5 (1974-75), 11-30. MR 0457466 |
| Reference:
|
[17] J. Vitória: Matricial norms and the differences between the zeros of determinants with polynomial elements.Lin. Alg. its Appl. 28 (1979), 279-283. MR 0549440, 10.1016/0024-3795(79)90139-3 |
| . |
