Your definitions reproduce the examples in
http://en.wikipedia.org/wiki/Khatri-Rao_product#Khatri-Rao_product :
( A=. (;~1 0 1) <;.1 (1+i.3 3) )
┌───┬─┐
│1 2│3│
│4 5│6│
├───┼─┤
│7 8│9│
└───┴─┘
( B=. (;~1 1 0) <;.1 (|: 1+i.3 3) )
┌─┬───┐
│1│4 7│
├─┼───┤
│2│5 8│
│3│6 9│
└─┴───┘
krp=. */block &.> NB. Khatri-Rao product
A krp B
┌─────┬─────┐
│1 2 │12 21│
│4 5 │24 42│
├─────┼─────┤
│14 16│45 72│
│21 24│54 81│
└─────┴─────┘
tsp=. (1 0 3 |: */)block&.>/block NB. Tracy-Singh product
A tsp B
┌─────┬───────────┬──┬─────┐
│1 2 │ 4 7 8 14│3 │12 21│
│4 5 │16 28 20 35│6 │24 42│
├─────┼───────────┼──┼─────┤
│ 2 4│ 5 8 10 16│ 6│15 24│
│ 8 10│20 32 25 40│12│30 48│
│ 3 6│ 6 9 12 18│ 9│18 27│
│12 15│24 36 30 45│18│36 54│
├─────┼───────────┼──┼─────┤
│7 8 │28 49 32 56│9 │36 63│
├─────┼───────────┼──┼─────┤
│14 16│35 56 40 64│18│45 72│
│21 24│42 63 48 72│27│54 81│
└─────┴───────────┴──┴─────┘
They are impressive!
On Tue, Apr 29, 2014 at 4:32 PM, Raul Miller <[email protected]> wrote:
> If I understand properly:
>
> Hadamard product is *
>
> Kroneker product is ([:,/[:,./"3*/)
>
> Or,
>
> block=: 1 : '[:,/[:,./"3 u'
> */ block
>
> There are of course other ways of defining this.
>
> Khatri-Rao product is A */block &.> B and works on a matrix of boxed
> matrices
>
> Tracy-Sigh product is (1 0 3 |: */)block&.>/block and also works on a
> matrix of boxed matrices
>
> Vector cross product gets interesting because it is typically defined on 3
> element vectors and there are at least two very distinct ways of
> generalizing that to vectors of other lengths.
>
> Anyways, the paper sounds interesting, and I'd like a copy if it's not too
> much trouble.
>
> Thanks,
>
> --
> Raul
>
> On Tue, Apr 29, 2014 at 3:17 PM, mikel paternain <[email protected]
> >wrote:
>
> > In a excellet review paper (see below [1]) Shuangzhe Liu & Götz Trenkler
> > show some results on matrix products:
> >
> > - Hadamard product
> > - Kroneker product
> > - Khatri-Rao product
> > - Tracy-Sigh product
> > - Khatri-Rao sum
> > - Tracy-Sigh sum
> > - Vector cross productSchur complement, etc.
> >
> > With this thread, we intend to create a collaborative work to find the
> > J-expressions that meet these products and sums.
> > If you want to collaborate, these will be published in next issue of
> > Journal of J (deadline May-31)
> > Thanks in advance,
> > Mikel
> > JoJ
> >
> >
> -----------------------------------------------------------------------------------------------------------------
> > [1] There is a free version on the webif you can not find it, we can send
> > you a copy
> >
> > HADAMARD, KHATRI-RAO, KRONECKER AND OTHER MATRIX PRODUCTS
> > Shuangzhe Liu & Götz Trenkler
> > International Journal of Infornation ans Systems Sciences
> > Vol. 4, N. 1, 160-177
> >
> >
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> >
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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