# when do $$A$$ and $$AA^T$$ have the same spectrum?

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, [...]

# Summer of languages

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 [...]

# new reading blog

I’ve started a separate blog to track my mathematical reading. Check it out, comment, and suggest material I might find interesting.

# Third week of the IBM internship

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 [...]

# Truncated SVD … how?

This question has been bothering me off and on for several months now: how *exactly* is the truncated SVD computed, and what is the cost? I’ve gathered that most methods are based on Krylov subspaces, and that implicitly restarted Arnoldi processes seem to be the most popular proposal … in what miniscule amount of literature [...]