TITLE: $^t$, $^\dagger$, $^*$, $^H$, $^⊤$, and $^T$ : Which is which, and what do each mean?
QUESTION [8 upvotes]: 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.

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?

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.

REPLY [3 votes]: If you use $A^\sf T$ and $A^\sf H$ respectively for the transpose and Hermitian conjugate of $A$ (which I prefer), then you are free to use $t,T,H,$ and * for other things, which is useful. The notation $A^+$ for the pseudo-inverse is aesthetically in line with this and more modern than $A^\dagger$.