Bra -- from Wolfram MathWorld

A bra <psi| is a vector living in a dual vector space to that containing kets |psi>. Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be considered as 1-vectors and 1-forms (or vice versa), although this is almost always done only in a finite-dimensional vector space. Considered as an inner product, the bra and ket form an angle bracket (bra+ket = bracket) <psi|psi>.

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Projection Operator -- from Wolfram MathWorld

One-Form -- from Wolfram MathWorld

Dirac Notation -- from Wolfram MathWorld

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