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I'm trying to multiply 2 Quaternion equations but I'm not sure if I'm multiplying them correctly. Here are the 2 equations:

$_1 = 2 − + + 3$

$_2 = −1 + + 4 − 2k$

and here is how I've multiplied these 2 equations:

$$q_1q_2 = ((2)(-1) - (-1)(1) - (1)(4) - (3)(-2))\\ + ((2)(1) - (-1)(-1) - (1)(-2) - (3)(4))i \\+ ((2)(4) - (-1)(-2) - (1)(-1) - (3)(1))j\\ + ((2)(-2) - (-1)(4) - (1)(1) - (3)(-1))k$$

When simplifying this, I get:

$$q_1q_2 = -8i + 4j + 2k $$

But calculating this using online counters I seem to be getting different results, have I calculated this correctly?

Strafe Ae
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Open Source
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1 Answers1

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This table will help you

$$ \begin{array}{|c|c|c|c|c|} \hline \cdot & 1 & i & j & k \\ \hline 1 & 1 & i & j & k \\ \hline i & i & -1 & k & -j \\ \hline j & j & -k & -1 & i \\ \hline k & k & j & -i & -1 \\ \hline \end{array} $$

So for example

$$ ji = -k $$

caverac
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