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lumen8r February 3rd, 2010 01:13 PM

Linear equation problem
 
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This doesn't seem too hard, but I just can't figure it out... any help would be greatly appreciated! Here it goes:

I have a matrix of measured data points (, i.e. rows and comlumns).
I know that the matrix is made up of the product of a column vector with a row vector , added to the product of a column vector of ones with another row vector

. In other words, and the , are the same within each row and the and , are the same within each column.

The are known (measured) and the , and are unknown. Therefore there are equations and unknown values. For example a matrix would provide 9 equations for 9 variables and there should be an exact solution. Any larger matrix would be overdetermined and should provide redundant equations for the , and (which could be used for calculating averages and estimating measurement errors).

How can the , and be calculated? Thanks again for any help or advice on this!

(for some reason the latex \overrightarrow did not work, so I used \overline to designate a vector...)

lumen8r March 9th, 2010 03:06 PM

Re: Linear equation problem
 
Hi Everyone - no replies yet? Maybe the problem is harder than I thought...?

Any thoughts or ideas would be very much appreciated, though: Maybe it was just a dumb question to ask? Maybe this is not solvable because of some fundamental/logical reasons? Or, if this is not obviously the case, maybe you know of another place where I could post this question?

Thanks again!


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