From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 8 Mar 2023 23:43:00 +0100
Subject: Restructure build system and directory structures

---
 src/math/matrices.org | 33 +++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 src/math/matrices.org

(limited to 'src/math/matrices.org')

diff --git a/src/math/matrices.org b/src/math/matrices.org
new file mode 100644
index 0000000..c968f8c
--- /dev/null
+++ b/src/math/matrices.org
@@ -0,0 +1,33 @@
+#+title:Matrix Properties
+#+setupfile: ../../math_options.org
+
+* 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*}
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