multrix/README.md

# Multrix

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

## Usage

To calculate the dot product of 2 matrices execute the `dot` command or `multrix` command in the output `bin` directory.

To calculate the cross product of 2 vectors execute the `cross` command or `multrix` command in the output `bin` directory.

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

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

```math
\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

```math
\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*}
```