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I have a matrix that I obtained from theoretical computation and I have another matrix which I obtained by actual data collection. How do I compare the two matrices? How do I state that one matrix is significantly different from the other?

I have looked into:

  • Frobenius Norm but I don't know what should be my threshold for comparison.
  • Looking at max and min deviation of one matrix from the other. But again, what's a good threshold?

I thought that to say one matrix varies significantly from the other, I would need to quantify the variance of those terms and compare how the deviation compares to the variance (or SD) but sadly, I don't have data for that and neither can I theoretically estimate any variances.

I am kind of lost in what would be a good metric.

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    This depends entirely on your application. Different metrics will be appropriate for different purposes.2012-11-29
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    Mathematical Statistics.2012-11-29
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    How was the matrix constructed and what do its entries represent?2012-11-29
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    @FlybyNight. The theoretical matrix is constructed using regression and the obtained matrix is well, obtained.2012-11-29
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    In that case, the metric will be constructed using metric theory and it's details will be found, somehow.2012-11-29

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