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Bug introduced in 12.3 or earlier, fixed in 13.0.

Suppose I have a normalized numerical 1D array, B1,

    B1 = {0.9269939990888411` - 0.22888585272824927` I, 
   1.3877787807814457`*^-17 + 0.` I, -2.7755575615628914`*^-17 - 
    1.8041124150158794`*^-16 I, 
   0.05746221176648221` + 
    0.10518387310098759` I, -1.3877787807814457`*^-17 - 
    9.020562075079397`*^-17 I, 
   0.0574622117664822` + 0.10518387310098762` I, 
   0.0574622117664822` + 0.10518387310098765` I, 
   2.0816681711721685`*^-17 - 3.469446951953614`*^-17 I, 
   0.` - 1.3877787807814457`*^-16 I, 
   0.057462211766482196` + 0.10518387310098765` I, 
   0.05746221176648217` + 0.10518387310098765` I, 
   2.7755575615628914`*^-17 - 6.938893903907228`*^-17 I, 
   0.05746221176648225` + 0.1051838731009876` I, 
   3.469446951953614`*^-17 - 3.469446951953614`*^-17 I, 
   5.0306980803327406`*^-17 - 
    3.469446951953614`*^-17 I, -0.04191842262180526` + 
    0.01851810652627404` I};

Then $Version == "12.3.0 for Mac OS X x86 (64-bit) (May 10, 2021)" gives the very sensible

Conjugate[B1] . B1
Transpose[Conjugate[B1]] . B1

as both 1. + 0. I. However

ConjugateTranspose[B1] . B1

gives 0.761773 - 0.353375 I, which is the same as what I get for B1.B1.

Questions:

  • What gives?
  • Is this known / expected behavior?
  • Is this a bug?
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  • 1
    $\begingroup$ ConjugateTranspose needs a matrix as input. If you give it a vector, it leaves it alone. Try: ConjugateTranspose[{1,I}] If this is a bug or a misuse of the command, I do not know. $\endgroup$
    – Daniel Huber
    Nov 12, 2021 at 17:39
  • $\begingroup$ Questions that might help diagnose or confirm this: Is Conjugate[Transpose[B1]]==ConjugateTranspose[B1] as the docs claim? Is B1==Transpose[B1]] ? Is Conjugate[B1]==Transpose[Conjugate[B1]] And do some or all of those work as expected if B1 is a well behaved matrix instead of a vector? $\endgroup$
    – Bill
    Nov 12, 2021 at 17:39
  • $\begingroup$ @DanielHuber the docs say "ConjugateTranspose[m] is equivalent to Conjugate[Transpose[m]]. »" which clearly isn't true in the above case. $\endgroup$
    – evanb
    Nov 12, 2021 at 17:41
  • $\begingroup$ Maybe it would help if you report this to [email protected] $\endgroup$
    – Daniel Huber
    Nov 12, 2021 at 17:43
  • $\begingroup$ @Bill, ConjugateTranspose[B1] == Conjugate[Transpose[B1]] gives False. B1==Transpose[B1] gives True. Conjugate[B1]==Transpose[Conjugate[B1]] gives True. To test the matrix case, you can try ConjugateTranspose[{B1, B1}] == Conjugate[Transpose[{B1, B1}]] which gives True. $\endgroup$
    – evanb
    Nov 12, 2021 at 17:43

1 Answer 1

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3
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This bug is resolved in version 13.0 ($Version == "13.0.0 for Mac OS X x86 (64-bit) (December 3, 2021)").

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