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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

7 votes
1 answer
307 views

Fundamental domain for two Grassmannians

Let $\pi_1, \pi_2$ be two $k$-dimensional subspaces of $\mathbb R^n$. Using elements of the orthogonal group $O(n)$, how much can we simplify $\pi_1, \pi_2$? Certainly there always exists $A \in O(n)$ …
Uzu Lim's user avatar
  • 903
3 votes
Accepted

Concentration inequality for the sample covariance matrix

A variant of this (taking $\frac1m$ instead of $\frac1{m-1}$ for the empirical covariance) is answered on Proposition 2.6, page 10 of https://arxiv.org/pdf/2110.06357.pdf .
Uzu Lim's user avatar
  • 903
3 votes
1 answer
801 views

Concentration inequality for the sample covariance matrix

I'd like to know if there is a concentration inequality for the sample covariance matrix that don't assume the knowledge of the true mean. Background. Given a probability distribution $\mu$ on $\math …
Uzu Lim's user avatar
  • 903