- #1

- 197

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[tex]

M_{i,j,k} = a_{i}b_{i}c_{i}

[/tex]

where the multiplication on the right is an outer product.

I've read that this is only possible if the matrix M has a rank of one, but I can find anything on how to actually decompose the matrix, only that it CAN BE done. Also, if M has rank one, does that mean that there is a "unique" decomposition? What if the rank is something other than one? In that case would it be possible to find a family of solutions?

Thanks for any help.