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...
Author: wj32
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...