The trace of $A$, an $N\times N$ matrix, is $\displaystyle\sum_{i=1}^N A_{ii}$.

What do you call $\displaystyle\prod_{i=1}^N A_{ii}$?

  • 5
    $\begingroup$ The product of the diagonal elements? ;-) Unless the matrix is triangular, then it's the determinant. $\endgroup$
    – JohnD
    Jan 9, 2014 at 16:22
  • 1
    $\begingroup$ For a triangular matrix, that is its determinant :P I don't know if there is a specific name for this operation. $\endgroup$
    – Joel
    Jan 9, 2014 at 16:22
  • 9
    $\begingroup$ For a general square matrix, the product is almost always not the determinant! $\endgroup$
    – Emily
    Jan 9, 2014 at 16:43
  • 3
    $\begingroup$ Just call it a multiplicative trace and leave a definition of this term somewhere in comments to your code; anyway, this function has too few applications to merit a name. $\endgroup$ Aug 18, 2016 at 11:45
  • 2
    $\begingroup$ People are especially interested in the trace because it is independent of the choice of basis. However, your $\prod_{i=1}^nA_{ii}$ does not enjoy this property, so its not as interesting. $\endgroup$
    – Kenta S
    Jan 1 at 1:42


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