| Title:
|
A treatment of a determinant inequality of Fiedler and Markham (English) |
| Author:
|
Lin, Minghua |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
737-742 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Fiedler and Markham (1994) proved $$ \Big (\frac {\mathop {\rm det } \widehat {H}}{k}\Big )^{ k}\ge \mathop {\rm det } H, $$ where $H=(H_{ij})_{i,j=1}^n$ is a positive semidefinite matrix partitioned into $n\times n$ blocks with each block $k\times k$ and $\widehat {H}=(\mathop {\rm tr} H_{ij})_{i,j=1}^n$. We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove $$ \mathop {\rm det }(I_n+\widehat {H}) \ge \mathop {\rm det }(I_{nk}+kH)^{{1}/{k}}.$$ (English) |
| Keyword:
|
determinant inequality |
| Keyword:
|
partial trace |
| MSC:
|
15A45 |
| idZBL:
|
Zbl 06644030 |
| idMR:
|
MR3556864 |
| DOI:
|
10.1007/s10587-016-0289-3 |
| . |
| Date available:
|
2016-10-01T15:20:10Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145868 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
