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Mathematics Wolfram Language

FullSimplify doesn't work as expected?

Hongyi Zhao

Posted 3 years ago

I tried with the following code snippet: up[\[Theta]_, \[CurlyPhi]] = {Cos[\[Theta]/2], E^(I\[CurlyPhi])Sin[\[Theta]/2]}; dn[\[Theta]_, \[CurlyPhi]] = {-E^(-I\[CurlyPhi])Sin[\[Theta]/2], Cos[\[Theta]/2]}; A = {up[\[Theta], \[CurlyPhi]], dn[\[Theta], \[CurlyPhi]]}; FullSimplify[ComplexExpand[ConjugateTranspose[A] . A ]] == IdentityMatrix[2] ConjugateTranspose[A] . A // ComplexExpand // FullSimplify == IdentityMatrix[2] The result is as follows: Why doesn't the last command work? Regards, Hongyi

I tried with the following code snippet:

up[\[Theta]_, \[CurlyPhi]] = {Cos[\[Theta]/2], 
   E^(I*\[CurlyPhi])*Sin[\[Theta]/2]};
dn[\[Theta]_, \[CurlyPhi]] = {-E^(-I*\[CurlyPhi])*Sin[\[Theta]/2], 
   Cos[\[Theta]/2]};
 A = {up[\[Theta], \[CurlyPhi]], dn[\[Theta], \[CurlyPhi]]};
FullSimplify[ComplexExpand[ConjugateTranspose[A] . A ]] == 
 IdentityMatrix[2]
ConjugateTranspose[A] . A // ComplexExpand // 
 FullSimplify == IdentityMatrix[2]

The result is as follows:

enter image description here

Why doesn't the last command work?

Regards, Hongyi

POSTED BY: Hongyi Zhao

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Hongyi Zhao

Posted 3 years ago

But it's also cumbersome for practical use.

POSTED BY: Hongyi Zhao

Hongyi Zhao

Posted 3 years ago

But I don't want to type the `()` each time. It seems that the only shortcut is like this: IdentityMatrix[2] == ConjugateTranspose[A] . A // ComplexExpand // FullSimplify