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Topic: Special matrix multiplication
Replies: 18   Last Post: Mar 22, 2012 5:12 AM

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 John D'Errico Posts: 9,130 Registered: 12/7/04
Re: Special matrix multiplication
Posted: Feb 4, 2012 7:27 AM

"Milos Milenkovic" <m.milenkovic@mathworks.com> wrote in message <jgj6ir\$rj7\$1@newscl01ah.mathworks.com>...
> Dear,
> suppose that we have two matrices, where each element has three values like follows:
>
> A=[(a1,b1,c1), (a2,b2,c2); (a3,b3,c3), (a4,b4,c4)]
> B=[(d1,e1,f1), (d2,e2,f2); (d3,e3,f3), (d4,e4,f4)]
>
> Now, I have to multiply these two matrices, and that is matrix C=A*B
>
> C=[ c11=(a1,b1,c1)*(d1,e1,f1)+(a2,b2,c2)*(d3,e3,f3), c12=(a1,b1,c1)*(d2,e2,f2)+(a2,b2,c2)*(d4,e4,f4); c21=(a3,b3,c3)*(d1,e1,f1)+(a4,b4,c4)*(d3,e3,f3), c22=(a3,b3,c3)*(d2,e2,f2)+(a4,b4,c4)*(d4,e4,f4)]
>
> where the most important here is the low for multiplying these three-value numbers is:
>
> (ai,bi,ci)*(di,ei,fi) = (bi*di+ei*(ai-bi), bi*ei , ei*ci+bi(fi-ei))
>
> Please, how to do this, I have a dozen of this matrices with 700x700 in dimension approximately.
> Best,
> Milos

While there is no magic that will let you do this for
no effort on your part, I still don't see the problem.

You can just write a function that takes a pair of triads,
and "multiplies" them by your rule.

Then just write another function that takes a pair of
matrices, and multiplies them, again as per your rule.

Its just a few loops. Whats the problem? You can even
build a special class for the purpose, where you define
a "multiply" to be anything you wish between class
members.

Its not even a big problem, but even if it was, you
eat even an elephantine computational problem one
byte at a time. Just start writing.

John