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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: What is the determinant of [] ?
Date: Mon, 25 Oct 2010 18:59:04 +0000 (UTC)
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"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <ia4jb9$rsq$1@fred.mathworks.com>...

> That's also a fair point, but it seems to me that "interpretations" like these are what motivated conventions like prod([])=1 in the first place. That is, it makes identities
> 
> prod([1,[]])=prod(1)*prod([])
> 
> and
> 
> sum([1,[]])=sum(1)+sum([])

Yes, there is the recursion relation that must be satisfied PROD and SUM, that can goes down to empty vector as I showed in the previous post.

That the reason prod([]) is logically 1. Another way to confirm the logic is

prod(a) = exp(sum(log(a)))

Is A is empty, log(A) is empty, sum([]) is 0 (because 0 is neutral element of +), and finally prod([]) = exp(0) = 1.

Bruno