You might be interested in http://www.jsoftware.com/books/pdf/brief.pdf
The coverage of matrix divide there is brief (only one sentence), of course. Alternatively, there is the vocabulary page http://www.jsoftware.com/help/dictionary/d131.htm which does indeed spell things out more along the lines of your current recommendation. Thanks, -- Raul On Wed, Apr 23, 2014 at 1:02 PM, alexgian <alexg...@blueyonder.co.uk> wrote: > Great info, thanks Roger. > If it was up to me, I'd DEFINITELY include that in the Vocabulary, is it > even documented anywhere else? > > > On 23 April 2014 17:33, Roger Hui <rogerhui.can...@gmail.com> wrote: > > > %. x for a vector x is the same as ($x)$%.,.x, and the key expression is > > %.,.x, the "matrix inverse" of a 1-column matrix. b=.y%.x on a tall > matrix > > x is solving a least-squares problem, the coefficients b that minimizes > the > > sum of squares of y - x +/ .* b . > > > > In addition, for a non-zero vector x, (%.x) +/ .* x is 1, a special case > of > > that (%.x)+/ .* x is an identity matrix, whence one can deduce that for > > vector x, %.x is x%+/x^2. > > > > ] x=: 7 ?.@$ 100 > > 94 56 8 6 85 48 66 > > %. x > > 0.00362137 0.00215741 0.000308202 0.000231152 0.00327465 0.00184921 > > 0.00254267 > > (%.x) +/ .* x > > 1 > > x % +/x^2 > > 0.00362137 0.00215741 0.000308202 0.000231152 0.00327465 0.00184921 > > 0.00254267 > > > > M=: 7 3 ?.@$ 100 > > (%.M) +/ .* M > > 1 5.55112e_17 _2.77556e_17 > > _1.21431e_16 1 1.11022e_16 > > _4.85723e_17 1.94289e_16 1 > > > > > > > > On Wed, Apr 23, 2014 at 9:13 AM, alexgian <alexg...@blueyonder.co.uk> > > wrote: > > > > > Just wondering: > > > %. 2 3 4 > > > 0.0689655 0.103448 0.137931 > > > > > > Which is fair enough enough at one level, I suppose, since the dot > > product > > > of the two arrays IS 1, but what system/equation is being solved here? > > > Obviously, there are infinite solutions. Why that one? > > > IOW, which "matrix" is being inverted here? > > > > > > Thanks > > > ---------------------------------------------------------------------- > > > 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
