# what is positively-semi-definite

positively-semi-definite was created in an attempt to improve my technical exposition skills. Additionally, it will provide some impetus for me to preserve my notes in a more permanent form (as opposed to scribling them down on a legal notepad which I will inevitably discard). I will use this medium to share some interesting things that I am learning about and some reflections on concepts which (I believe) I already understand.

I chose the name positively-semi-definite for two reasons:

A reduction to familiarity: A positively semi-definite matrix (over $\mathbf{R}$) has eigenvalues $\lambda_i \geq 0$. While studying an algorithm/system, proving that some key matrix is positively semidefinite generally gives an immediate piercing insight into the way things will ‘probably’ behave. This is also the fundamental goal of every technical note: cutting through the noise to reduce complicated thoughts into a set of familiar intuitions.

An expression of uncertainty: To be semi-definite about something is to be uncertain. This works on two levels:

Statistics is the science of uncertainty. Most of my notes will probably be about mathematical statistics. This is what I understand best, and is what I will be learning about for the forseeable future.

Epistemic Uncertainty. These are my ‘known unknowns’ and my ‘unknown unknowns’. Although I will only write about topics that I am reasonably informed about, there is always scope to go one level deeper. I will never be able to speak from a place of absolute authority and there will always be some uncertainty inherent to publishing my opinions publicly: I will always be positively semi-definite about what I write. I hope that subjecting my technical opinions to a very public ‘peer review’ process will educate me about the perspectives which I missed.