From: robert bristow-johnson on
On Jul 6, 10:42 pm, spop...(a)speedymail.org (Steve Pope) wrote:
> Greg Berchin  <gberc...(a)comicast.net.invalid> wrote:
>
> >Every time I see this argument raise its ugly head in comp.dsp, I find myself
> >shaking my head and thinking:  "Because that's the way we've always done it" is
> >rarely a legitimate reason for continuing to do things wrong.
>
> I wonder which mathematician decided that matrices are indexed from one
> instead of zero?
>
> There is so much matrix theory published that is dependent upon
> this decision that it's impossible to un-do it in the world of
> math literature.

i do not think, nor have ever believed, that this is an "either or"
thing. it's not a dichotomy. it not a forced choice. no one needs
to choose between one convention (the long established matrix index
convention) and another (the "Dykstra" convention
http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF ). in fact,
it's just a generalization. neither convention need be adopted and,
as we do with non-causal impulse responses, we can start counting from
some negative index.

it's a generalization to or an extension to the present way of doing
things in MATLAB. and even though it doesn't favor any particular
origin in use, it *does* favor the present 1-based origin in MATLAB
because every new array created *defaults* to having 1 as the origin
for every dimension. the only way to change it would be to call this
"reorigin()" function (similarly to reshape()) or to create a non-1
based array from other non-1 based arrays. this makes it backward
compatible. old code would not break with this extension to the
language implemented.

r b-j
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