Gosh. Matrices "Comport themselves". I like it. Surely an array of rank > 2 is a "space"
Quoting Roger Hui <[email protected]>: > Donald McIntyre, *Language as an intellectual tool: From hieroglyphics to > APL, *IBM Systems Journal, Volume 30, Number 4, 1991, page 569: > > In 1848 Cayley showed that the combined effect of two rotations could be > represented as the product of two quaternions, and shortly afterwards > Sylvester (in the year he introduced the term *matrix*) pointed out that any > number of rotations can be represented by a single rotation about one axis. > As we would now say: each rotation can be represented by a matrix, and the > product of these matrices is a matrix completely describing the combined > rotation, whose axis is an eigenvector of this matrix, and the angle of > rotation can be found from the corresponding eigenvalue. By 1855 Cayley > used matrix product (calling it the *composition* of matrices), and in his > memoir of 1858 he wrote: "It will be seen that matrices comport themselves > as single quantities; they may be added, multiplied, or compounded together, > etc.: the law of addition of matrices is precisely similar to that for the > addition or ordinary algebraical quantities; as regards their multiplication > (or composition), there is the peculiarity that matrices are not in general > convertible; it is nevertheless possible to form the poewrs (positive or > negative, integral or fractional) of a matrix ..." [17] In this memoir he > uses Sylvester's latent roots (eigenvalues), but without naming them. > > [17] A. Cayley, "A Memoir on the Theory of Matrices", Royal Society of > London, *Philosophical Transactions **148*, 17-37 (1858). Reprinted in > *Collected > Mathematical Papers **2*, No. 152 (1889). > > > > On Tue, Oct 25, 2011 at 5:42 PM, <[email protected]> wrote: >> According to this source, you're right. >> >> http://www.etymonline.com/index.php?term=matrix >> >> S >> >> >> Quoting Devon McCormick <[email protected]>: >> >>> I believe I heard (maybe from Ken?) that matrix is from the Latin "Mater" >>> (mother) because of the various factorization methods that create smaller >>> matrixes from an original one. >>> >>> On Tue, Oct 25, 2011 at 6:15 PM, Alexander Mikhailov <[email protected] >> wrote: >>> >>>> >>>> >>>> Having word "matrix" (where it came from?..) and tradition in J to name >>>> things with non-traditional names (verb, noun), I'd vote for orthotope. >>>> Unmistakeable, succinct. >>>> >>>> >>>> >>>> ----- Original Message ----- >>>> From: Henry Rich <[email protected]> >>>> To: Programming forum <[email protected]> >>>> Cc: >>>> Sent: Sunday, October 23, 2011 7:10 PM >>>> Subject: [Jprogramming] The word for arrays of rank > 2 >>>> >>>> 'cube' was suggested. Raul objected that a cube should have all axes of >>>> equal length. >>>> >>>> 'cuboid' has been used in Ye Dic (in the description of ;.0). According >>>> to Wikipedia a cuboid should have rank 3. And the word seems strained. >>>> >>>> 'hyperrectangle' is used, but it's a fifty-cent word for a ten-cent > idea. >>>> >>>> A fancier word is 'orthotope'. Great if you're a Greek scholar. >>>> >>>> Also, 'box', which would be perfect if we weren't using it already. >>>> >>>> How about 'brick'? or 'block'? >>>> >>>> I like 'brick', followed by 'cube'. >>>> >>>> Henry Rich >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>> >>> >>> >>> -- >>> Devon McCormick, CFA >>> ^me^ at acm. >>> org is my >>> preferred e-mail >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >> >> >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
