From 561bac75579391c14e47eaccfabdf9eda98855da Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 27 Jul 2022 18:13:20 +0200
Subject: Initial commit

---
 math/matrices.org | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 math/matrices.org

(limited to 'math/matrices.org')

diff --git a/math/matrices.org b/math/matrices.org
new file mode 100644
index 0000000..a7ba58b
--- /dev/null
+++ b/math/matrices.org
@@ -0,0 +1,32 @@
+#+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