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This is just an opinion question about notations.

Having learned the basics of bra-ket notation and using the ESC, as far as I can tell, ESC is just plain better, at least when dealing with finite bases. Using bras and kets, you can represent and manipulate states using scalars, vectors (functions), one-forms (dual functions), and operators, but using ESC you can extend this very easily to any kind of tensor.

I haven't done any ESC where the bases involved were countably or uncountably infinite, so maybe that's where bras and kets become more advantageous - but on the other hand, it would surprise me if there's not some simple extension of the rules of the ESC that allows it to account for these types of bases (eg., an index appearing as superscript and subscript implies integration with respect to that index, so ESC becomes EIC).

So basically, it seems to me that bra-ket notation is great for linear algebra, but ESC is great for tensor analysis, which includes linear algebra, and it also works just as well as bras and kets for linear algebra before worrying about higher order tensors. So it's better.

Is there some obvious advantage to bras and kets that isn't occuring to me right now (this thought occured to me about 10 minutes ago, so I haven't really considered it that much)? What are people's opinions?

-HJ Farnsworth