Timeline for Norm of triangular truncation operator on rank deficient matrices
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2017 at 21:08 | comment | added | Mikael de la Salle | By duality, the triangular truncation $T$ has the same norm for the operator norm and the Schatten $1$-norm (trace norm). So $T$ has norm $\simeq \log(n)$ on $S^1_n$. An explicit example for the lower bound is provided by the $n \times n$ matrix with $1$'s everywhere. It has $1$-norm equal to $n$, but its triangular truncation has norm $\simeq n \log n$. | |
| Sep 5, 2017 at 16:43 | comment | added | Exodd | do you know if there is a Schatten norm-1 bound on the norm of the operator, when performed on matrices? | |
| Nov 24, 2014 at 1:36 | vote | accept | sb945 | ||
| Sep 30, 2014 at 19:57 | history | edited | Mikael de la Salle | CC BY-SA 3.0 |
added 1366 characters in body
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| Sep 27, 2014 at 23:31 | history | edited | Christian Remling | CC BY-SA 3.0 |
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| Sep 27, 2014 at 5:21 | history | answered | Mikael de la Salle | CC BY-SA 3.0 |