From: Kent Crispin <kent@bywater.songbird.com>
Date: Mon, 27 Oct 1997 11:22:25 +0800
To: Cypherpunks Distributed Remailer <cypherpunks@ssz.com>
Subject: Re: Orthogonal (fwd)
In-Reply-To: <199710270042.SAA01737@einstein.ssz.com>
Message-ID: <19971026191312.56933@bywater.songbird.com>
MIME-Version: 1.0
Content-Type: text/plain



On Sun, Oct 26, 1997 at 06:42:14PM -0600, Jim Choate wrote:
> > I do believe the use of the term this way was inspired by the 
> > notion of a 'basis' in a vector space -- a set of orthogonal
> > vectors that span the space, ideally, unit vectors.
> 
> Can you better define the term 'basis'?

This is basic linear algebra:

V a vector space -- the set of all (s1,s2,s3,...,sn), where si is an
element of the set of reals.  A set of vectors {v1,v2,...,vm} in V is
linearly independent if there is no set of scalars {c1,c2,...,cm} with
at least one non-zero element such that sum(ci*vi) == 0.  A set of
vectors S spans a vector space V iff every element of V can be expressed
as a linear combination of the elements of S.   Finally, a basis for 
V is a linearly independent set of vectors in V that spans V.  A 
space is finite dimensioned if it has a finite set for a basis.  The 
standard basis (or natural basis) for a vector space of dimension n 
is th set of vectors

(1,0,0,...0)
(0,1,0,...0)
(0,0,1,...0)