Skip to content

A Cluttered Mind

Math, anecdotes, recipes.

  • Roughly two posts per year
  • First post on

Posts per year

Data for this chart is available in the table below
Posts per year
Year starting Posts
2021 5
2022 5
2023 1
2024 2

Any gaps could be due to errors when fetching the blog’s feed.

Most recent posts

Chain Rule for Maps
$\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}$ Chain Rule for Map between Open Subsets of Euclidean Space Let $M$ be an open subset of $\R^m$, $N$ be an open subset of $\R^n$, and $O$ be an open subset of $\R^p$. Let …
On , 602 words
Harvard Way to Define Trace
$\newcommand\F{\mathbb{F}}\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}\newcommand\tr{\operatorname{trace}}\newcommand\End{\operatorname{End}}$ The trace of a sqaure matrix $A$ is defined to be the sum of the elements along the diagonal. A basic fact is that for any invertible matrix $M$, \begin{equation}\tag{*} \tr(M^{-1}AM) = \tr(A). \end{equation} …
On , 440 words
Singular Value Decomposition
$\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}$ The singular value decomposition is usually defined for a matrix. Here, we will show directly that any linear map between inner product spaces has a singular value decomposition. The singular value decomposition of a …
On , 694 words