[r-t] Falseness
Richard Smith
richard at ex-parrot.com
Fri Sep 24 10:32:57 UTC 2004
Robin Woolley wrote:
[...]
> The basic ratio is one of the pair multiplied by the inverse of the other.
> (The inverse is that permutation resulting in rounds). So:
>
> X(AC) = inv(C).A X(BD) = inv(D).B
Can I briefly raise a notational issue here? Because
transposition of rows is not commutative (by which I mean
that A transposed by B is not, in general, the same as B
transposed by A), the order of multiplication is important.
This means, when we see the expression A.B we need to know
whether this means B transposed by A, or A transposed by B.
This is purely a matter of convention, and, as such, some
people prefer one meaning whilst others choose the other
meaning.
In this email, it's clear that Robin is using A.B to mean B
transposed by A. On the other hand, in my earlier email on
singles in minor, I was using the opposite convention --
that A.B means A transposed by B. I certainly don't expect
everyone to start using the same convention -- I'm not even
sure it would be desireable -- but can I request that in the
future, people specify which convention they're using?
Richard
More information about the ringing-theory
mailing list