Gary
GaryVasco
Posts: 3,352
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Post by Gary on Sept 5, 2016 0:20:56 GMT
Vasco,
On p. 292 at midpage, Needham has
$\hspace{5em}\frac{1}{\sqrt{2}}(1 + \textbf{J})\frac{1}{\sqrt{2}}(1 + \textbf{I}) = \frac{1}{2}(1 + \textbf{I} + \textbf{J} - \textbf{K})$.
Do you agree that this should be written
$\hspace{5em}\frac{1}{\sqrt{2}}(\textbf{1} + \textbf{J})\frac{1}{\sqrt{2}}(\textbf{1} + \textbf{I}) = \frac{1}{2}(\textbf{1} + \textbf{I} + \textbf{J} - \textbf{K})$ ?
It is doubtless a typo, but the difference is important.
Gary
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Post by Admin on Sept 5, 2016 11:28:49 GMT
Gary
Since on page 291 second paragraph Needham simplifies the notation so that the scalar part of the quaternion is written as $v$ rather than $v1$ then it seems to me that this is not an error. We just need to remember that if (in expressions like the one in your post), we replace $I,J,K$ by their equivalent matrices, as given at the bottom of p.291, we must replace $v$ by $v\times$ (the 2x2 identity matrix).
So, it seems to me that the $1$ in your expression can be present or omitted, whichever the writer prefers for reasons of clarity.
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Sept 5, 2016 13:01:37 GMT
Vasco,
I see that you are right; Hamilton's quaternion notation mixes the scalar and the vector. No error. But I think it would be nicer to use a notation that is consistent within an equation. I don't think the 1 can be omitted, but it could be in boldface or not.
Gary
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Post by Admin on Sept 5, 2016 13:15:08 GMT
Gary
Sorry for my misleading comment. What I meant was that if the term is not equal to unity, say $k$ where $k\neq1$ then we must write $k$ or $k$1, but when $k=1$ then we can write 1 or 1 or even 11. I agree with you.
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Sept 5, 2016 13:20:42 GMT
Vasco,
I see.
Gary
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