Let me put this here, as it's so simple that everyone can take a look at it. I must be blind not to see my misconclusion, but look for yourself(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]a^TA^\dag b := (a^TAb)^*[/tex] be the definition of the adjoint [tex]A^\dag[/tex].

I thus conclude that

[tex] \underbrace{a^T A^\dag }_{\tilde a^T} \underbrace{B^\dag b}_{\tilde b} = \tilde a^T B^\dag b \stackrel{\text{ex vi termini}}{=}(\tilde a^T B b)^* = (a^T A^\dag B b)^*[/tex]

[tex]\ldots \qquad= a^T A^\dag \tilde b \stackrel{\text{ex vi termini}}{=}(a^T A \tilde b)^* = (a^T A B^\dag b)^*[/tex]

Which is generally true and thus [tex]A^\dag B = A B^\dag[/tex] which is nonsense!?

Edit: Darn, I got the definition of the adjoint wrong, so my conclusion is correct.

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# Adjoint magic? Absurdity from nothing?

Can you offer guidance or do you also need help?

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