I think this question's answer(s) will be of profound use to the future generation of human beings who happen to stumble upon the website *math.stackexchange.com*.

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What are the differences between $^t$, $^\dagger$, $^\*$, $^H$, and $^T$. Further, to which is which associated, and are there some cases where one is used for both?

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I'd like to see definitions for each group of superscript symbols and how $T$ the transformation and $A$ the matrix are related. I feel it would be good to have this as an answer here for all eyes to see.