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Results tagged with oa.operator-algebras
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user 5963
Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
11
votes
Accepted
Are the banded versions of a positive definite matrix positive definite?
No. The matrix
$M = \begin{bmatrix}5 & 4 & 4 \\\\ 4 & 5 & 4 \\\\ 4 & 4 & 5\end{bmatrix} = \begin{bmatrix}2 & 2 & 2\end{bmatrix}\begin{bmatrix}2 \\\\ 2 \\\\ 2\end{bmatrix} + I$
is positive definite, …
- 8,501
2
votes
What is the dual of an semidefinitely representable (SDR) cone?
Edited in response to Alex Monras's correction in the comments:
The cone $\mathcal{K}^*$ is always SDR: this is just the conic / homogeneous version of Theorem 5.57 in the new book "Semidefinite Opti …
- 8,501