This URL has a page from Hermann Weyl's 1939 book "The classical groups: their invariants and representations," in which k-vector is used to describe an n-tuple with entries from a number field k http://books.google.com/books?id=zmzKSP2xTtYC&pg=PA18&lpg=PA18&dq=k-vector+h... On Mon, Mar 15, 2010 at 5:16 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 3/14/10, Fred lunnon <fred.lunnon@gmail.com> wrote:
Indeed, the point I had made at the GA site was that the Clifford / Grassmann algebra usage should be deprecated, partly on these grounds. But now I'm beginning to wonder if said ambiguity resulted only from my confusing "k-vector" with "k-tuple", etc?
Searching on "n-vector" turned up the following on the first page
http://mathworld.wolfram.com/n-Vector.html << n-Vector An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. >>
http://webpages.dcu.ie/~oriordae/matrix-problems.pdf << Q1: Let x be an n-vector and A a n x n matrix. ... >>
http://ptp.ipap.jp/link?PTP/49/1451/ << Critical Behavior of the Anisotropic Classical n-Vector Model ... The critical exponents of the anisotropic classical model with n components are investigated in the 1/n-expansion. >>
http://kr.cs.ait.ac.th/~radok/math/mat5/algebra12.htm << Let (y_1, ··· , y_n) (4) be the vectors of this space. The vectors (y1, ··· , yn, 0) (5) form a vector space X' consisting of (n + 1)-vectors. n-vectors (4) are independent if and only if the corresponding vectors (5) are independent, ... >>
In contrast --- but in contexts which are more remote from mainstream linear algebra --- http://www.farcaster.com/papers/sm-thesis/node24.html uses "n-vector" to mean a set of n vectors.
http://ptp.ipap.jp/link?PTP/49/1451/ << Critical Behavior of the Anisotropic Classical n-Vector Model ... The critical exponents of the anisotropic classical model with n components are investigated in the 1/n-expansion. >> This and several more concern a percolation model in which matrices in O(n) --- effectively Cl(n,0,0) versors --- are associated with nodes of a lattice.
No doubt searching on "m-vector", "3-vector" would find plenty more. It's noteworthy that the Hestenes(?) "k-vector" usage is absent from these pages!
Fred Lunnon
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