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Results tagged with linear-algebra
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user 493804
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
0
answers
56
views
What is the closed form of a polyhedral cone's dual cone?
A polyhedral cone can be defined as
$$
\mathcal{K} = \{x~|~Ax\preceq 0\},
$$
where $A \in \mathbb{R}^{m \times n}$, $x\in \mathbb{R}^n$ and $\preceq$ denotes component-wise less than and equal to.
The …
- 71
5
votes
1
answer
289
views
Analytical form for the nuclear norm of an $n \times n$ matrix
I get the follow equation in a paper. Let $A \in \mathbb{R}^{2 \times 2}$, then $M = A^TA$ is a positive semi-definite matrix, the nuclear norm of $A$ is:
$$ \Vert A \Vert_* = \sqrt{\operatorname{tr}( …
- 71