multrix/README.md

# Multrix

Matrix multiplication calculator; calculates the cross & dot products of matrices and vectors.

## Usage

The `multrix` command can calculate both dot or cross products if given the respective command line argument. If no valid commandline argument is given the program will ask which type of calculation should be made.

## installation

To install using nimble:

```sh
nimble install https://git.inamatrix.xyz/array-in-a-matrix/multrix
```

To install using pacman:

```sh
git clone https://git.inamatrix.xyz/array-in-a-matrix/multrix
cd multrix
makepkg si
```

## 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

$$
\begin{align*}
\vec{A} \times \vec{B} =
\begin{vmatrix}
i & j & k\\
a_1 & a_2 & a_3\\
b_1 & b_2 & b_3
\end{vmatrix} = (a_2b_3-a_3b_2)i + (a_3b_1-a_1b_3)j+(a_1b_2-a_2b_1)k
\end{align*}
$$