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Any account of Dirac's bra-ket vectors depends critically on your understanding of vector spaces. Unfortunately, we have no idea as to how familiar you are with such concepts and cannot take on the task of educating you in vector spaces. I suggest you look at the Wikipedia article at https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

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Q: Give a concise account of Dirac's 'bra' and 'ket' vectors?
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