Timeline for What does $\mathbb E_V \max_{x \in V,\,\|x\|=1} x^T Ax$ evaluate to when $V$ is random $k$-dim suspace of $\mathbb R^n$ and $A$ is fixed psd matrix?

8 events

when toggle format	what		by	license	comment
Dec 26, 2021 at 2:33	history	edited	Michael Hardy	CC BY-SA 4.0	deleted 33 characters in body
Dec 25, 2021 at 14:50	history	edited	dohmatob	CC BY-SA 4.0	edited body
Dec 25, 2021 at 14:20	history	edited	dohmatob	CC BY-SA 4.0	added 230 characters in body
Dec 25, 2021 at 13:15	comment	added	dohmatob		Yes, that's a typo that I couldn't correct due to time limit for editing comments. But ma point still remains, about simplifying by introducing an intermediate step.
Dec 25, 2021 at 12:48	comment	added	Dustin G. Mixon		@dohmatob - In your notation, $\lambda$ is the vector of square roots of eigenvalues of $A$.
Dec 25, 2021 at 10:04	vote	accept	dohmatob
Dec 25, 2021 at 10:02	comment	added	dohmatob		Also, in the final calculation, just before applying J. Tropp's (4.6), it might help to write $\\|\Lambda^{1/2} G\\|^2_{2 \to 2} = \\|B \odot G\\|^2_{2 \to 2}$, where $B = \lambda \otimes 1_k \in \mathbb R^{n \times k}$, where $\lambda \in \mathbb R^n$ is the vector of eigenvalues of $A$ (in any order).
Dec 25, 2021 at 3:01	history	answered	Dustin G. Mixon	CC BY-SA 4.0