Bulletin of the American Mathematical Society

Geršgorin theorems by Householder's proof

J. L. Brenner

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 74, Number 3 (1968), 625-627.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183529651

Mathematical Reviews number (MathSciNet)
MR0223074

Zentralblatt MATH identifier
0159.03501

Citation

Brenner, J. L. Geršgorin theorems by Householder's proof. Bull. Amer. Math. Soc. 74 (1968), no. 3, 625--627. https://projecteuclid.org/euclid.bams/1183529651


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References

  • 1. A. Brauer, Limits for the characteristic roots of a matrix, Duke Math. J. 19 (1952), 75-91.
  • 2. J. L. Brenner, New root-location theorems for partitioned matrices, Summary Report, #748, MRC, Madison, Wis., 1967; SIAM J. Appl. Math. 16, No. 3 (1968).
  • 3. D. G. Feingold and R. S. Varga, Block diagonally dominant matrices and generalizations of the Geršgorin circle theorem, Pacific J. Math. 12 (1962), 1241-1250.
  • 4. S. Geršgorin, Über die Abgrenzung der Eigenwerte einer Matrix, Izv. Akad. Nauk SSSR 7 (1931), 749-754.
  • 5. A. S. Householder, The theory of matrices in numerical analysis, Blaisdell, New York, 1964.
  • 6. M. Marcus and H. Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, Mass., 1964.
  • 7. A. M. Ostrowski, Sur les conditions générales pour la regularité des matrices, Rend. Mat. e Appl. 10 (1951), 1-13.
  • 8. O. Taussky, A recurring theorem on determinants, Amer. Math. Monthly 56 (1948), 672-676.

See also

  • Errata: Errata. Bull. Amer. Math. Soc., Volume 74, Number 4 (1968), 767--768.