A programming language reference is not the place to teach a subject. In this case, you can always consult a textbook on linear algebra or appropriate pages in the Wikipedia.
On Wed, Apr 23, 2014 at 10:52 AM, alexgian <[email protected]>wrote: > > The information and more are in the vocabulary page for %. > > Well, yes, but so tersely and compactly expressed that you have to know the > long answer before you understand it! I did look at the Vocab page, but > didn't "get it", that's why I posted. > > It needed Roger's somewhat more expanded explanation for those of us that > are somewhat slower on the uptake. That's why I said the Vocab could use a > touch up. It is NOT user friendly, more of an ultra-coded reference. Of > course, you might not see it this way, but I'd bet most newcomers would. > > And it's not as if there is a longer explanation somewhere else, is there? > Well, other than this thread, I mean... :) > > > > On 23 April 2014 18:17, Roger Hui <[email protected]> wrote: > > > The information and more are in the vocabulary page for %. > > http://www.jsoftware.com/help/dictionary/d131.htm . > > > > > > On Wed, Apr 23, 2014 at 10:02 AM, alexgian <[email protected] > > >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 <[email protected]> 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 <[email protected] > > > > > > 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 > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
