Bounds of matrices with regard to an hermitian metric

Werner Gautschi

Compositio Mathematica (1954-1956)

  • Volume: 12, page 1-16
  • ISSN: 0010-437X

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Gautschi, Werner. "Bounds of matrices with regard to an hermitian metric." Compositio Mathematica 12 (1954-1956): 1-16. <http://eudml.org/doc/88815>.

@article{Gautschi1954-1956,
author = {Gautschi, Werner},
journal = {Compositio Mathematica},
keywords = {linear algebra, forms, polynomials},
language = {eng},
pages = {1-16},
publisher = {Kraus Reprint},
title = {Bounds of matrices with regard to an hermitian metric},
url = {http://eudml.org/doc/88815},
volume = {12},
year = {1954-1956},
}

TY - JOUR
AU - Gautschi, Werner
TI - Bounds of matrices with regard to an hermitian metric
JO - Compositio Mathematica
PY - 1954-1956
PB - Kraus Reprint
VL - 12
SP - 1
EP - 16
LA - eng
KW - linear algebra, forms, polynomials
UR - http://eudml.org/doc/88815
ER -

References

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  1. A.C. Aitken. [1] Deterininants and matrices, University Math. Texts, vol. 1, 7th edition. Edinburgh & London1951. Zbl0047.01803
  2. [2] W. Givens.Fields of values of a matrix, Bull. Amer. Math. Soc., vol. 58 (1952), p. 53. Zbl0048.25003MR47004
  3. P.R. Halmos. [3] Finite dimensional vector spaces, Annals of Mathematics Studies, nr. 7, Princeton1942. (P. 91, line 10: instead of |y|2 read ∥y∥2 p. 91, line 15: instead of R[αβ(x, y)] read R[αβ(x, y)].) Zbl0063.01886
  4. H.L. Hamburger and M.E. Grimshaw. [4] Linear Transformations in n-dimensional vector space, Cambridge University Press, Cambridge1951. Zbl0043.32504MR41355
  5. F. Hausdorff. [5] Der Wertevorrat einer Bilinearform, Math. Z., Bd. 3 (1919), pp. 314—316. Zbl47.0088.02JFM47.0088.02
  6. M.R. Hestenes and M.L. Stein. [6] The Solution of Linear Equations by Minimization, NBS-NAML Report 52—45, Washington, D.C., 1951. Zbl0242.65043
  7. W. Ledermann. [7] On an upper limit for the latent roots of a certain class of matrices, J. Lond. Math. Soc., vol. 12 (1937), pp. 12—18. Zbl0016.09903JFM63.0038.02
  8. J. Von Neumann and H.H. Goldstine. [8] Numerical inverting of matrices of high order, Bull. Amer. Math. Soc., vol. 53 (1947), pp. 1021—1099. Zbl0031.31402
  9. A. Ostrowski. [9] Un nouveau théorème d'existence pour les systèmes d'équations, C. R. Acad. Sci. Paris, t. 232 (1951), pp. 786—788. Zbl0042.06302
  10. [10] Leçons sur la résolution des systèmes d'équations, to appear in the series of the cahiers scientifiques at Gauthier-Villars, Paris. 
  11. M.H. Stone. [11] Linear Transformations in Hilbert Space and their applications to Analysis, Amer. Math. Soc. Coll. Publ., vol. XV (1932). Zbl0005.40003MR1451877JFM58.0420.02
  12. O. Toeplitz. [12] Das algebraische Analogon zu einem Satze von Fejér, Math. Z., Bd. 2 (1918), pp. 187—197. Zbl46.0157.02JFM46.0157.02

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