| Title:
|
Schur complements of diagonally dominant matrices (English) |
| Author:
|
Carlson, David |
| Author:
|
Markham, Thomas L. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
1979 |
| Pages:
|
246-251 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
15A15 |
| idZBL:
|
Zbl 0423.15008 |
| idMR:
|
MR529512 |
| DOI:
|
10.21136/CMJ.1979.101601 |
| . |
| Date available:
|
2008-06-09T14:33:36Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101601 |
| . |
| Reference:
|
[1] Arthur Albert: Conditions for positive and nonnegative definiteness in terms of pseudo inverses.SIAM J. Appl. Math. 17 (1969), 434-440. MR 0245582, 10.1137/0117041 |
| Reference:
|
[2] David Carlson: Matrix decompositions involving the Schur complement.SIAM J. AppL Math. 28(1975), 577-587. MR 0382304, 10.1137/0128047 |
| Reference:
|
[3] Douglas Crabtree: Applications of $M$-matrices to nonnegative matrices.Duke Math. J., 33 (1966), 197-208. MR 0186677, 10.1215/S0012-7094-66-03324-2 |
| Reference:
|
[4] Douglas Crabtree, Emilie V. Haynsworth: An identity for the Schur complement of a matrix.Proc. Amer. Math. Soc. 22 (1969), 364-366. MR 0255573, 10.1090/S0002-9939-1969-0255573-1 |
| Reference:
|
[5] Miroslav Fiedler, Vlastimil Pták: On matrices with nonpositive off-diagonal elements and positive principal minors.Czech. Math. J. 12 (87) (1962), 382-400. MR 0142565 |
| Reference:
|
[6] Miroslav Fiedler, Vlastimil Pták: Diagonally dominant matrices.Czech. Math. J. 17 (92) (1967), 420-433. MR 0215869 |
| Reference:
|
[7] F. R. Gantmacher: The theory of matrices. Vol. I.Chelsea, New York, 1959. |
| Reference:
|
[8] Emilie V. Haynsworth: Determination of the inertia of a partitioned hermitian matrix.Lin. Alg. Appl. 1 (1967), 73-82. MR 0223392, 10.1016/0024-3795(68)90050-5 |
| Reference:
|
[9] M. S. Lynn: On the Schur product of $H$-matrices and nonnegative matrices, and related inequalities.Proc. Camb. Phil. Soc. 60 (1964), 425 - 431. MR 0166204, 10.1017/S0305004100037932 |
| Reference:
|
[10] Marvin Marcus, Henryk Mine: A Survey of Matrix Theory and Matrix Inequalities.Allyn and Bacon, Boston, 1964. MR 0162808 |
| Reference:
|
[11] Olga Taussky: A recurring theorem on determinants.American Mathematical Monthly, 56 (1949), 672-676. MR 0032557, 10.1080/00029890.1949.11990209 |
| . |
