What happens when you sample columns from a matrix whose columns all have roughly the same norm? It’s clear that you should have some kind of concentration: say if you sample \(\ell\) of \(n\) columns, then the Frobenius norm of the resulting matrix, appropriately scaled, should be a very good approximation of the Frobenius norm … Continue reading Sampling models and vector sums
The applied side of approximation theory is like black magic to me: even if I don’t want to do research in the area, at least I respect it enough to find it interesting. So, I recommend bit-player’s post on Nick Trefethen’s Chebfun package. Especially check out the links (Trefethen’s an engaging author).
I’m looking at products like \(\mat{G}^t \mat{A} \mat{G}\) where the columns of \(\mat{G}\) are (nonisotropic) normal vectors. Specifically, I’d like to know the distribution of the eigen/singular-values of this product. Surprisingly, I was unable to find any results in the literature on this, so I started reading Gupta and Nagar to see if I could … Continue reading Verify these matrix properties (easy and fun)
Wooo woooo! I just found George Gently‘s coming (came?) back for 2011. I also found out that there was a 2010 season! Too bad Netflix doesn’t have it yet 🙁 Here’s the first Netflix review I (remember having) ever wrote. I was that impressed by the show. Hope I can share that enthusiasm. For some … Continue reading George Gently
Looks like I’ll be visiting U. Michigan for a week or so at the end of October. What does one do on such a visit? I’ve been invited to give a talk, but that doesn’t occupy more than an afternoon… I spent this morning reading through some of the literature on subspace tracking, then wound … Continue reading A sequence whose closure is the unit circle
Because a picture’s worth a thousand words: The matrix involved is a projection, not some numerically unstable thing like the Hilbert matrix. You suck at linear algebra, Mathematica.
I still haven’t hammered out the database issues, but I’m tired of my little vacation (i.e. several months!) from posting, so I’m going ahead with the relocation. At some unspecified time in the future (once I figure out the technical details), I’ll migrate the database over from the old location. That site’ll still be up, … Continue reading ChapterZero’s relocated