I’ve been off Being Human (the original UK version) for a while now. I stopped watching after the first episode of season 3, in part because the American version came out and I got into that before it started circling the drain, and in part because Mitchell gets on my damned last nerve. Now I’m … Continue reading We play the long game here
I was reading, of all things, a romance novel when I came across this famous excerpt from Childe Harold’s Pilgrimage: Roll on, thou deep and dark blue Ocean – roll! Ten thousand fleets sweep over thee in vain; Man marks the earth with ruin – his control Stops with the shore; – upon the watery … Continue reading Roll On
Jeff Salyards is doing an Ask Me Anything (AMA) on Reddit tonight at 5 PCT. I started reading his debut novel, Scourge of the Betrayer, a couple of weeks ago, but couldn’t get into it for one reason or another. Maybe I was just coming off of an urban fantasy binge, and the relatively heavier … Continue reading Monument
Recall our old friend the \(\|\cdot\|_{\infty \rightarrow 1}^*\) norm (from the first version of this website, which I still haven’t gotten around to merging into the current iteration). Given a matrix \(\mat{A},\) it is a measure of the energy in the smallest expansion of \(\mat{A}\) in terms of rank one sign matrices: \[ \|\mat{A}\|_{\infty \rightarrow … Continue reading A list of \(\|\cdot\|_{\infty \rightarrow 1}^*\) problems
Well damn. It’s been a long while. Time for another post about my not having posted in a while. I’m wrapping up my internship here at IBM, preparing the exit talk on my research. It’s entitled “New results on the accuracy of randomized spectral methods.” I’ll put up the talk after we’ve wrapped up the … Continue reading Drawing to a close at IBM
Let \(\mat{F},\mat{G}\) be positive definite matrices (do they have to be definite?) and \(0 \leq p \leq 2.\) Show that \[ \tr\left(\mat{F}^{p/2} – \mat{G}^{p/2}\right) \leq \frac{p}{2} \tr\left((\mat{F} – \mat{G})\mat{G}^{p/2 – 1}\right). \] I’m working on it. See if you can get a proof before I do 🙂
There are matrices for which the spectrum of \(\mat{A}\) and \(\mat{A}\mat{A}^T\) are identical. As an example, take \[ \mat{A} = \begin{pmatrix} \frac{1}{2} & 0 & \frac{1}{2} & 0 \\ 0 & \frac{1}{2} & 0 & \frac{1}{2} \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}. \] Freaky, … Continue reading when do \(A\) and \(AA^T\) have the same spectrum?
This summer’s the summer of languages for me. I’m learning R piecemeal, because I’m working on a data analytics project that requires a lot of statistical analysis: learning a new language is a bother, but the unprecedented amount of statistical packages available for R justifies the investment. I also decided to dive into Julia, despite … Continue reading Summer of languages
I’ve started a separate blog to track my mathematical reading. Check it out, comment, and suggest material I might find interesting.
I’m working on an internal project that motivated me to look into survival analysis. Cool stuff, that. Essentially, you have a bunch of data about the lifetimes of the some objects and potentially related covariates, and from that data you’d like to estimate the functional relationship between the lifetimes and the covariates, in the form … Continue reading Third week of the IBM internship