regarding this answer.

it also seems to me that this result should have been obtained and published somewhere or documented in a book somewhere, but i dunno where. if someone knows of a reference, i would love to know about it.


  • $\begingroup$ right away, i think i am informed of a big error in the swapping of the summation order. $\endgroup$ Sep 6 '18 at 21:32
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    $\begingroup$ As the commentor of (math.se) dxiv stated, unless the matrix is symmetric; $A = A^{T}$, the equality wont hold. Cause the left side is summing the lower triangular elements while the right side is summing the upper triangular elements. This assumes that for the element $a_{nk}$, $n$ stands for rows and $k$ stands for $columns$. $\endgroup$
    – Fat32
    Sep 6 '18 at 22:57
  • $\begingroup$ @Fat32, i think i groked this upper and lower triangle thing and i fixed the limits in my summations. i hope it's right now, but i would still like someone else to verify. $\endgroup$ Sep 7 '18 at 0:10
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    $\begingroup$ I just checked it (on the surface) and it seems ok. $\endgroup$
    – Fat32
    Sep 7 '18 at 10:04
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    $\begingroup$ thank you @Fat32 $\endgroup$ Sep 9 '18 at 3:04

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