1.6 KiB
1.6 KiB
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:
nimble install https://git.inamatrix.xyz/array-in-a-matrix/multrix
To install using pacman:
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*}