On means of positive definite matrices

Theodore Töllis

Czechoslovak Mathematical Journal (1987)

  • Volume: 37, Issue: 4, page 628-641
  • ISSN: 0011-4642

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Töllis, Theodore. "On means of positive definite matrices." Czechoslovak Mathematical Journal 37.4 (1987): 628-641. <http://eudml.org/doc/13673>.

@article{Töllis1987,
author = {Töllis, Theodore},
journal = {Czechoslovak Mathematical Journal},
keywords = {power mean; positive definite matrices; Hadamard product; inequalities; geometric and arithmetic means; comparison of matrices; linear models},
language = {eng},
number = {4},
pages = {628-641},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On means of positive definite matrices},
url = {http://eudml.org/doc/13673},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Töllis, Theodore
TI - On means of positive definite matrices
JO - Czechoslovak Mathematical Journal
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 4
SP - 628
EP - 641
LA - eng
KW - power mean; positive definite matrices; Hadamard product; inequalities; geometric and arithmetic means; comparison of matrices; linear models
UR - http://eudml.org/doc/13673
ER -

References

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  1. T. Ando, 10.1016/0024-3795(79)90179-4, Linear Algebra Appl. 26 (1979) 203-241. (1979) Zbl0495.15018MR0535686DOI10.1016/0024-3795(79)90179-4
  2. E. F. Beckenbach, R. Bellman, Inequalities, Springer-Verlag 1965. (1965) Zbl0186.09605MR0192009
  3. Achim Clausing, 10.2307/2321725, American Mathematical Monthly, 89 (1982) 314-330. (1982) Zbl0491.26009MR0653510DOI10.2307/2321725
  4. K. H. Hardy J. E. Littlewood, and K. Pólya, Inequalities, Cambridge University Press 1952. (1952) MR0046395
  5. Erwin Lutwak, On Power Means of Positive Quadratic Forms, Linear Algebra Appl. 57 (1984) 13-19. (1984) Zbl0529.15012MR0729257
  6. I. Schur, Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen, J. Reine Angew. Math. 140 (1911) 1 - 28. (1911) Zbl42.0367.01
  7. Czeslaw Stepniak, Ordering of Nonnegative Definite Matrices with Applications to Comparison of Linear Models, Linear Algebra and Appl. 70 (1985) 67-71. (1985) Zbl0578.15019MR0808532
  8. K. P. H. Styan, 10.1016/0024-3795(73)90023-2, Linear Algebra and Appl. 6 (1973) 217-240. (1973) Zbl0255.15002MR0318177DOI10.1016/0024-3795(73)90023-2
  9. Theodore Tollis, An inequality involving determinants of positive definite hermitian matrices, Abstracts of AMS, January 1985. (1985) 

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