| Title:
|
Nested matrices and inverse $M$-matrices (English) |
| Author:
|
Stuart, Jeffrey L. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
537-544 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the $LU$- and $QR$-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse $M$-matrices with symmetric, irreducible, tridiagonal inverses. (English) |
| Keyword:
|
nested matrix |
| Keyword:
|
tridiagonal matrix |
| Keyword:
|
inverse $M$-matrix |
| Keyword:
|
principal minor |
| Keyword:
|
determinant |
| Keyword:
|
$QR$-factorization |
| MSC:
|
15A09 |
| MSC:
|
15A15 |
| MSC:
|
15B05 |
| idZBL:
|
Zbl 06486963 |
| idMR:
|
MR3360443 |
| DOI:
|
10.1007/s10587-015-0192-3 |
| . |
| Date available:
|
2015-06-16T18:04:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144286 |
| . |
| Reference:
|
[1] Berman, A., Plemmons, R. J.: Nonnegative Matrices in the Mathematical Sciences.Classics in Applied Mathematics 9 SIAM, Philadelphia (1994). Zbl 0815.15016, MR 1298430 |
| Reference:
|
[2] : The On-Line Encyclopedia of Integer Sequences.http://oeis.org (2010). |
| Reference:
|
[3] Weisstein, E. W.: Fibonorial.From MathWorld---A Wolfram Web Resource,\ http://mathworld.wolfram.com/Fibonorial.html. |
| . |
