In the previous post, I talked about the HRT conjecture as a rather natural statement about phase space. A signal can be moved in time. It can also be moved in frequency. Moving it in time changes …

The mathematics community has recently been effervescing with plenty of AI usage stories (notably Terence Tao, nonetheless) ¹. In the latest such development, a long-standing conjecture was disproved …

Suppose we are given a linear dynamical system $$G=(A,B,C,D)$$ (recall that a linear system is an input $$x$$ to output $$y$$ map such that $$y_k = Cx_k + Du_k, x_{k+1}=Ax_k+Bu_k$$), and $$G$$ has …

Well, if one were to cut to the chase, it appears to be because of the Central Limit Theorem (CLT). However, there is more underlying structure under the hood as to why the Gaussians seem to be the …

Consider an $$n+1$$ dimensional matrix as follows:

$$ A = \begin{pmatrix} \frac{\pi^2}{6} & 1 & \frac{1}{4} & ... & \frac{1}{n^2} \\ 1 & \frac{\pi^2}{6} & \frac{1}{4} & ... & \frac{1}{n^2} \\ \vdots & …

Almost always we hear about classification or machine learning problems, the go-to methods to solve the problem are neural networks, or multi-layered percetrons (MLP). Now function approximation …

When I took the course on Real Analysis, it made me very nervous. I was having fever dreams from the past when I took undergraduate real analysis and the epsilon-delta definitions just did not make a …

In my last post I touched upon the intuition behind topological compactness. We as engineers often hear about the word ‘compact’ as a soft gatekeeping tool from doing serious …

This is a non-mathematical note on what I understand about compactness and what it means for a set or a space to be compact. The open cover definition is one that can be found in any textbook, but …

It might seem out of place that in the world of big data, finding a singular parameter’s estimate could be interesting. Quite the contrary – point estimation problems are one of the most …