Hey guys, I am wondering if the following relationships hold for all operators A, regardless of whether they are linear or non-linear.(adsbygoogle = window.adsbygoogle || []).push({});

A^{-1}A = AA^{-1}= I

[A,B] = AB - BA

A|a_{n}> = λ_{n}|a_{n}>, where n ranges from 1 to N, and N is the dimension of the vector space which has an orthogonal basis |a_{n}>.

Just one other question. Which is the more general definition of the adjoint (hermitian conjugate) A† of an operator A: (v, Au) = (A†v, u) or A† = (A*)^{T}?

I think it's the first one. The second one is a special case of the first which is valid if the vectors v and u are matrices. Your thoughts?

Let's see if you can make a dumbass like me learn some maths!

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# Miscellaneous questions on operators

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