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Concept information

theoretical physics aspects > quantum mechanics > operator > self-adjoint operator

Terme préférentiel

self-adjoint operator  

Définition(s)

  • In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map A (from V to itself) that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian matrix, i.e., equal to its conjugate transpose A∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Self-adjoint_operator)

Concept(s) générique(s)

Concept(s) associé(s)

Synonyme(s)

  • Hermitian operator

Traductions

URI

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