| Title:
|
On an extension of Fekete’s lemma (English) |
| Author:
|
Chon, Inheung |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
63-66 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that if a real $n \times n$ non-singular matrix ($n \ge m$) has all its minors of order $m-1$ non-negative and has all its minors of order $m$ which come from consecutive rows non-negative, then all $m$th order minors are non-negative, which may be considered an extension of Fekete’s lemma. (English) |
| MSC:
|
15A15 |
| idZBL:
|
Zbl 0954.15005 |
| idMR:
|
MR1676845 |
| . |
| Date available:
|
2009-09-24T10:19:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127467 |
| . |
| Reference:
|
[1] I. Chon: Lie group and control theory.Ph.D. Thesis, Louisiana State University, 1988. |
| Reference:
|
[2] M. Fekete: Ueber ein Problem von Laguerre.Rendiconti del Circolo Matematico di Palermo 34 (1912), 92–93. |
| Reference:
|
[3] F. R. Gantmacher: The Theory of Matrices vol. 1 and vol. 2.Chelsea Publ. Comp., New York, 1960. MR 1657129 |
| Reference:
|
[4] S. Karlin: Total Positivity vol. 1.Stanford University Press, 1968. MR 0230102 |
| Reference:
|
[5] C. Loewner: On totally positive matrices.Math. Zeitschr. 63 (1955), 338–340. Zbl 0068.25004, MR 0073657, 10.1007/BF01187945 |
| Reference:
|
[6] G. Pólya and G. Szegö: Aufgaben and Lehrsätze aus der Analysis vol. 2.Springer-Velag, 1964. |
| Reference:
|
[7] A. M. Whitney: A reduction theorem for totally positive matrices.J. d’Analyse Math. Jerusalem 2 (1952), 88–92. Zbl 0049.17104, MR 0053173, 10.1007/BF02786969 |
| . |
