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*To*: Cypherpunks Distributed Remailer <[email protected]>*Subject*: Re: Orthogonal (fwd)*From*: Kent Crispin <[email protected]>*Date*: Sun, 26 Oct 1997 19:13:12 -0800*In-Reply-To*: <[email protected]>; from Jim Choate on Sun, Oct 26, 1997 at 06:42:14PM -0600*References*: <[email protected]>*Sender*: [email protected]

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)

**References**:**Re: Orthogonal (fwd)***From:*Jim Choate <[email protected]>

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