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Re: [SCICOMP] Kronecker tensor produkt



On Wed, 07 Jun 2000, Martin E. Nielsen wrote:

> Hej,
> 
> > > Måske (!) er det lidt off-topic, men findes der et
> > > symbol for Kroneckers
> > > tensor produkt? eller skriver man blot 'kron(a,b)'?
> > I alle mine år: har ikke hørt om det?
> > Hvad er det for noget stads?
> Hvis du har de to matricer A og B:
> A = [a11 a12 a13]
>     [a21 a22 a23]
> 
> B = [b11 ... b1n]
>     [ .   .   . ]
>     [bm1 ... bmn]
> (formen af B er egentlig unødvendig!)
> 
> er kron(A,B) = [a11*B a12*B a13*B]
>                [a21*B a22*B a23*B]
> Du ganger simpelthen matricen B på samtlige af A's elementer. Den
> resulterende matrix har i dette tilfælde størrelsen: (2*m) x (3*n)
> 
> Jeg ved ikke hvad man normalt bruger det til, men jeg har brugt det i
> forbindelse med en Gauss Newton implementering til opdatering af vægtene
> i et neuralt netværk.

Du bruger det også i forbindelse med billed restaurering.  Et NxN pixel billede
giver et flot N^2 x N^2 lineært næsten-singulært (ill-conditioned)
ligningssystem som man så kan iterere på.

Jeg har (med success ;)  brugt  et ``o'' med et ``x'' i, altså bolle-kryds,
eller hvad du nu vil kalde det, til Kronecker produktet.   Jeg tror ikke der er
nogen anerkendt standard, bare sørg for at nævn hvad symbolet betyder.

-- 
................................................................
: sslug@sslug  : And I see the elder races,         :
:.........................: putrid forms of man                :
:   Jakob Østergaard      : See him rise and claim the earth,  :
:        OZ9ABN           : his downfall is at hand.           :
:.........................:............{Konkhra}...............:


 
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