The physical meaning of multiplying a matrix by a vector, and how it works on several special matrices.

We think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.

A selection of our most-read and -shared articles of the past month

The iterated logarithm comes up occasionally in the analysis of algorithms. It's also useful for giving a compact way to describe unimaginably large numbers.

The additive persistence of a number is related to iteratively casting out nines. Multiplicative persistence is analogous but more interesting.

The binomial number system represents numbers as (a, b, c) where every number is the sum C(a, 1) + C(b, 2) + C(c, 3).

Positional number systems typically have a integer base, but irrational and even complex bases are possible. The golden ratio was the first irrational base.

Two ways of computing the Euler-Mascheroni constant, one much better than the other. Discussing software that's even better.

Suppose you need to write software to compute the sine function. You were told in a calculus class that this is done using Taylor series—it's not, but that's another story—and so you start writing…

We roll up our sleeves and start to deal with matrices

Powers of the golden ratio are nearly integers. This post explains why. Also, these integers are the sum of two Fibonacci numbers.

Understanding and Implementing Brant’s Tests in Ordinal Logistic Regression with Python

A detailed guide on controlling overfitting and increasing the stability of your models.

The physical meaning of multiplying two matrices and how it works on several special matrices.

How to choose an estimate that minimizes the squared relative errors to each of the data points. The

Sometimes the solution to a complicated problem is remarkably simple.

A simple approximation to the sinc function, a function that comes up constantly in signal analysis.

Entropy increases as system states become more uniform and decreases as they become further from uniform.

I saw a post online this morning that recomended the transformation I could see how this could be very handy. Often you want something like a logarithmic scale, not for the exact properties of the…

When you patch two functions together, how smooth does the patch need to be? How do you measure smoothness?