src | ||
.gitignore | ||
LICENSE | ||
multrix.nimble | ||
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
$$ \begin{align*} A \cdot B = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \ a_{21} & a_{22} & \cdots & a_{1n} \ \vdots & \vdots & \ddots & \vdots \ a_{m1} & a_{m2} & \cdots & a_{mn} \ \end{bmatrix} \cdot \begin{bmatrix} b_{11} & b_{12} & \cdots & b_{1p} \ b_{21} & b_{22} & \cdots & b_{1p} \ \vdots & \vdots & \ddots & \vdots \ b_{n1} & b_{n2} & \cdots & b_{np} \ \end{bmatrix}
\begin{bmatrix}
a_{11}b_{11} + \cdots + a_{1n}b_{n1} & a_{11}b_{12} + \cdots + a_{1n}b_{n2} & \cdots & a_{11}b_{1p} + \cdots + a_{1n}b_{np} \
a_{21}b_{11} + \cdots + a_{2n}b_{n1} & a_{21}b_{12} + \cdots + a_{2n}b_{n2} & \cdots & a_{21}b_{1p} + \cdots + a_{2n}b_{np} \
\vdots & \vdots & \ddots & \vdots \
a_{m1}b_{11} + \cdots + a_{mn}b_{n1} & a_{m1}b_{12} + \cdots + a_{mn}b_{n2} & \cdots & a_{m1}b_{1p} + \cdots + a_{mn}b_{np} \
\end{bmatrix}
\end{align*}
Cross Product
$$
\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*}