312
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

On the eigenvalues of principal submatrices of normal, hermitian and symmetric matrices

, &
Pages 69-78 | Received 20 Jan 1992, Published online: 30 May 2007

References

  • Ahlfors , L. 1979 . Complex Analysis , McGras Hill . 3rd Edition
  • Au-Yeung , Y. H. and Poon , Y. T. 1979 . 3 × 3 orthostochastic martices and the convexity of generalized numerical ranges . Linear Algebra Appl , 27 : 69 – 79 .
  • Fan , K. and Pall , G. 1957 . Imbedding conditions for Hermitian and normal matrices . Canad. J. Math , 9 : 298 – 304 .
  • Horn , R. and Johnson , C. R. 1990 . Matrix Analysis , Cambridge University Press .
  • Johnson , C. R. and Robinson , H. A. 1981 . Eigenvalue inequalities for principal submatrices . Linear Algebra Appl , 37 : 11 – 22 .
  • Deutsch , E. and Hochstadt , H. 1978 . On cauchy′s inequalities for hermitian matrices . Amer. Math. Monthly , 85 : 486 – 487 .
  • Nylen , P. and Tam , T. Y. 1991 . Some inequalities involving the eigenvalues of a hermitian matrix . manuscript , 85
  • Poon , Y. T. and Tsing , N. K. 1987 . Inclusion relations between orthostochastic matrices and products of pinching matrices . Linear and Multilinear Algebra , 21 : 253 – 259 .
  • Thompson , R. C. 1966 . Principal submatrices of normal and hermitian matrices . Illinois J. Math , 10 : 297 – 308 .
  • Thompson , R.C. 1979 . Principal submatrices II: The upper and lower quadratic inequalities . Linear Algebra Appl , 1 : 211 – 243 .
  • Thompson , R.C. 1968 . Principal submatrices III: Linear inequalities . J. Res. Nat. Bur. Standards Sect. B , 72B : 7 – 22 .
  • Thompson , R.C. 1969 . Principal submatrices IV: On the independence of the eigenvalues of different principal submatrices . Linear Algebra Appl , 2 : 355 – 374 .
  • Thompson , R.C. 1972 . Principal submatrices VIII . Rocky Mountain J. Math. , 2 : 97 – 110 .
  • Thompson , R.C. 1989 . Lecture Notes from Johns Hopkins University Lecture Series , 2
  • Thompson , R.C. 1991 . The eigenvalue spread of a Hermitian matrix and its principal submatrices . manuscript , 2

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.