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Archived: 07 Aug 2014, 09:49
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Shaun Culver
Site Admin
Joined: 25 Feb 2008, 13:32 Posts: 106 Location: Cape Town, South Africa
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 Quaternions
So the following relations are suppose to follow from  : But, for instance, multiplying through by  in the relation  yields: This is my problem, how can  . I suspect that I've missed some vital detail, perhaps some subtly to do with the commutation law.
_________________ “Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there.”
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26 May 2008, 02:55 |
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Sameed Zahoor
Joined: 12 Mar 2008, 10:57 Posts: 69 Location: India
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 Re: Quaternions
Multiplication in quatenionic algebra should be considered an "operation" for conceptual clarity.(e.g multiplication by iota in the complex plane signifies an anticlockwise rotation by a right angle) Suppose we have  When the operator i acts on ij the result will be the same as i acting on -ji.That is,  (this is called pre multiplying by i) Now we know,  Pre multiplying b/s by ij we have  or  (because ij and -ji are the same operators) This is called post-multiplication by i. You have pre-multiplied by i on the LHS but post-multiplied on the RHS which has led to this error.
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26 May 2008, 09:16 |
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Shaun Culver
Site Admin
Joined: 25 Feb 2008, 13:32 Posts: 106 Location: Cape Town, South Africa
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 Re: Quaternions
Thank you Sameed. The ordering of symbols is essential. Viewing these entities as "operators" makes this clearer. I have many, many more questions; too many to ask here though - I'll have to save up to buy a book on quaternions (and octonions).
_________________ “Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there.”
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29 May 2008, 16:17 |
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