added formulas
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README.md
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README.md
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@ -13,3 +13,46 @@ The `multrix` command can calculate both dot or cross products if given the resp
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## installation
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## installation
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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`.
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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`.
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## Math
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### Dot Product
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$$
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\begin{align*}
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A \cdot B =
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\begin{bmatrix}
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a_{11} & a_{12} & \cdots & a_{1n} \\
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a_{21} & a_{22} & \cdots & a_{1n} \\
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\vdots & \vdots & \ddots & \vdots \\
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a_{m1} & a_{m2} & \cdots & a_{mn} \\
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\end{bmatrix}
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\cdot
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\begin{bmatrix}
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b_{11} & b_{12} & \cdots & b_{1p} \\
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b_{21} & b_{22} & \cdots & b_{1p} \\
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\vdots & \vdots & \ddots & \vdots \\
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b_{n1} & b_{n2} & \cdots & b_{np} \\
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\end{bmatrix}
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=
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\begin{bmatrix}
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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} \\
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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} \\
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\vdots & \vdots & \ddots & \vdots \\
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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} \\
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\end{bmatrix}
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\end{align*}
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$$
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## Cross Product
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$$
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\begin{align*}
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\vec{a} \times \vec{b} =
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\begin{vmatrix}
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i & j & k\\
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a_1 & a_2 & a_3\\
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b_1 & b_2 & b_3
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\end{vmatrix} = (a_2b_3-a_3b_2)i + (a_3b_1-a_1b_3)j+(a_1b_2-a_2b_1)k
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\end{align*}
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$$
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