From ef87bf3338adf5d78209f64e302d76f311d5f236 Mon Sep 17 00:00:00 2001
From: array-in-a-matrix <git@arrayinamatrix.xyz>
Date: Tue, 17 Jan 2023 16:57:41 -0500
Subject: [PATCH] added formulas

---
 README.md | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/README.md b/README.md
index f9d6fe7..40fa730 100644
--- a/README.md
+++ b/README.md
@@ -13,3 +13,46 @@ The `multrix` command can calculate both dot or cross products if given the resp
 ## installation
 
 The program requires no dependencies other than the nim standard library. Just run `make` in the root of the project and run the executables in `bin`.
+
+## Math
+
+### Dot Product
+
+$$
+\begin{align*}
+A \cdot B =
+\begin{bmatrix}
+a_{11} & a_{12} & \cdots & a_{1n} \\
+a_{21} & a_{22} & \cdots & a_{1n} \\
+\vdots & \vdots & \ddots & \vdots \\
+a_{m1} & a_{m2} & \cdots & a_{mn} \\
+\end{bmatrix}
+\cdot
+\begin{bmatrix}
+b_{11} & b_{12} & \cdots & b_{1p} \\
+b_{21} & b_{22} & \cdots & b_{1p} \\
+\vdots & \vdots & \ddots & \vdots \\
+b_{n1} & b_{n2} & \cdots & b_{np} \\
+\end{bmatrix}
+=
+\begin{bmatrix}
+a_{11}b_{11} + \cdots + a_{1n}b_{n1} & a_{11}b_{12} + \cdots + a_{1n}b_{n2} & \cdots & a_{11}b_{1p} + \cdots + a_{1n}b_{np} \\
+a_{21}b_{11} + \cdots + a_{2n}b_{n1} & a_{21}b_{12} + \cdots + a_{2n}b_{n2} & \cdots & a_{21}b_{1p} + \cdots + a_{2n}b_{np} \\
+\vdots & \vdots & \ddots & \vdots \\
+a_{m1}b_{11} + \cdots + a_{mn}b_{n1} & a_{m1}b_{12} + \cdots + a_{mn}b_{n2} & \cdots & a_{m1}b_{1p} + \cdots + a_{mn}b_{np} \\
+\end{bmatrix}
+\end{align*}
+$$
+
+## Cross Product
+
+$$
+\begin{align*}
+\vec{a} \times \vec{b} =
+\begin{vmatrix}
+i & j & k\\
+a_1 & a_2 & a_3\\
+b_1 & b_2 & b_3
+\end{vmatrix} = (a_2b_3-a_3b_2)i + (a_3b_1-a_1b_3)j+(a_1b_2-a_2b_1)k
+\end{align*}
+$$