From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001 From: Thomas Albers Date: Wed, 8 Mar 2023 23:43:00 +0100 Subject: Restructure build system and directory structures --- math/matrices.org | 32 -------------------------------- 1 file changed, 32 deletions(-) delete mode 100644 math/matrices.org (limited to 'math/matrices.org') diff --git a/math/matrices.org b/math/matrices.org deleted file mode 100644 index a7ba58b..0000000 --- a/math/matrices.org +++ /dev/null @@ -1,32 +0,0 @@ -#+TITLE:Matrix Properties -#+SETUPFILE: ../math_options.org -#+LATEX_HEADER: \usepackage{bm} -#+LATEX_HEADER: \usepackage{mathtools} - -* Disclaimer -This site as of now just a technology demonstration and its claims -should not be taken as true (even though I myself am pretty confident -they are) -* Basic properties -\begin{align*} -A + B = B + A -\end{align*} -* Dot product -\begin{align*} -(A^\text{T})^\text{T} &= A\\ -(A + B)^\text{T} &= A^\text{T} + B^\text{T}\\ -(AB)^\text{T} &= B^\text{T}A^\text{T} -\end{align*} -* Transpose -\begin{align*} -\bm{a} \cdot \bm{b} &= \overline{\bm{b}} \cdot \bm{a}\\ -\bm{a} \cdot \bm{b} &= \bm{a}^\text{T} \bm{b} -\end{align*} - -* Hermitian transpose -\begin{align*} -A^\ast &= \left[\overline{a_{ij}}\right]\\ -(\lambda A)^\ast &= \left[\overline{\lambda a_{ij}}\right] = \overline{\lambda} \left[a_{ij}\right]^\ast = \overline{\lambda}\,\overline{A}\\ -A^\dag &= (A^\ast)^\text{T}\\ -A^{\dag\dag} &= A -\end{align*} -- cgit v1.2.3