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Results tagged with positivity
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user 8430
40
votes
Accepted
Wanted: Positivity certificate for the AM-GM inequality in low dimension
The following paper:
Fujiwara, Kazumasa, and Tohru Ozawa. Identities for the Difference between the Arithmetic and Geometric Means, (2014).
proves the following representation for odd $n$:
\be …
- 28.6k
6
votes
Accepted
On a trace condition for positive definite $2\times 2$ block matrices
For any unitarily invariant norm it can be shown that
\begin{equation*}
\|X\| = \left\Vert
\begin{bmatrix}
A & C\\
C^* & B
\end{bmatrix}
\right\Vert \le \|A\| + \|B\|.
\end{eq …
- 28.6k
6
votes
Accepted
Non-negative decomposition of a non-negative matrix
This seems to be the well-known (and difficult) task of computing the nonnegative rank of a matrix.
It seems that the true complexity of computing the nn-rank is unknown, while verifying whether nn-r …
- 28.6k