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A linear operator (including a matrix) acting on a non-zero *eigenvector* preserves its direction but, in general, scales its magnitude by a scalar quantity *λ* called the *eigenvalue* or characteristic value associated with that eigenvector. Even though it is normally used for linear operators, it may also extend to nonlinear operations, such as Schroeder functional composition, which evoke linear operations.

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Need help understanding product of Kronecker delta function with an outer product

I need help solving the the below expression which is from the book Modern Quantum Mechanics by J. J. Sakurai and Jim Napolitano. $$A=\sum_{a''}\sum_{a'}|a''\rangle a'\delta_{a'a''}\langle a'| =~?$$ I …
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