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by Ciro Santilli (@cirosantilli, 37)

Linear operator

 Home Mathematics Area of mathematics Algebra Linear algebra Linear map
 0 By others on same topic  0 Discussions  Updated 2025-05-07  +Created 1970-01-01  See my version
We define it as a linear map where the domain is the same as the image, i.e. an endofunction.
Examples:
  • a 2x2 matrix can represent a linear map from R2 to R2, so which is a linear operator
  • the derivative is a linear map from C∞ to C∞, so which is also a linear operator
  • Table of contents
    • Adjoint operator Linear operator

Adjoint operator (A†)

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Linear operator
Given a linear operator A over a space S that has a inner product defined, we define the adjoint operator A† (the † symbol is called "dagger") as the unique operator that satisfies:
∀v,w∈S,<Av,w>=<v,A†w>
(1)

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  • Adjoint operator
  • Bra-ket notation
  • Hermitian operator
  • Schrödinger equation
  • Spectrum (functional analysis)

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