## PAE patch updated for Windows 10

This patch allows you to use more than 3/4GB of RAM on an x86 Windows system. Works on Windows Vista SP2, Windows 7 SP0, Windows 7 SP1, Windows 8, Windows 8.1 a...

## F# code: memoize a recursive function

In this article we’ll look at how to memoize a general function f : ('a -> 'b) -> 'a -> 'b in F#, along with some interesting applications. Gener...

## Horn’s inequality for singular values via exterior algebra

$$\DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\Id}{Id}$$Horn’s inequality states that for any two compact operato...

## New web host

I’ve moved this website to Fresh Roasted Hosting because the previous host was awful in terms of reliability and support. The whole process only took a fe...

## PAE patch updated for Windows 8.1

Note: An updated version for Windows 10 is available. This patch allows you to use more than 3/4GB of RAM on an x86 Windows system. Works on Windows Vista SP2, ...

## Line integrals: 3. Applications to complex analysis

$$\newcommand{\bbc}{\mathbb{C}} \newcommand{\Int}{\operatorname{Int}}$$Navigation: 1. Exact, conservative and closed forms | 2. Locally exact forms and singul...

## Line integrals: 2. Locally exact forms and singular homology

Navigation: 1. Exact, conservative and closed forms | 2. Locally exact forms and singular homology | 3. Applications to complex analysis As in part 1, $$E,F$$ a...

## Line integrals: 1. Exact, conservative and closed forms

Navigation: 1. Exact, conservative and closed forms | 2. Locally exact forms and singular homology | 3. Applications to complex analysis The line integral is a ...

## First-order ODEs, matrix exponentials, and det(exp)

Last time we derived a formula for the derivative of the matrix exponential. Here we will be focusing instead on the expression $$D\exp(x)u=\exp(x)u=u\exp(x),$$...

## Fréchet derivative of the (matrix) exponential function

$$D\exp(x)u = \int_0^1 e^{sx}ue^{(1-s)x}\,ds.$$ This intriguing formula expresses the derivative of the exponential map on a Banach algebra as an integral. In...