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Results tagged with inequalities
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user 36687
for questions involving inequalities, upper and lower bounds.
4
votes
1
answer
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An inequality involving operator and trace norms
Consider two square matrices $A, B \in \mathbb{R}^{n \times n}$ and let $\| \cdot\|_1$ and $\|\cdot\|$ be, respectively, the trace norm (the sum of singular values) and the usual operator norm (the ma …
- 1,731
1
vote
Accepted
Hanson-Wright inequality with random matrix
Let $x \sim N(0,I_n)$. For any independent rank-1 projection $A$, conditioned on $A$, we have
$$x^T A x \sim \chi^2_1.$$ So unconditionally, $x^T A x = O(1)$ with high probability.
Now, let $A = \fr …
- 1,731