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A matrix $H$ is Hermitian if $H ^\dagger = H$. A matrix $U$ is Unitary if $U^\dagger=U^{-1}$.

My question is:

  1. Why do we name matrices of such properties Hermitian and Unitary? These names are non-intuitive and have nothing to do with these properties.

  2. Who named them?

  3. Possible citation of first appearance in paper?

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  • $\begingroup$ Hermitian is for Charles Hermite (1822-1901), french mathematician. $U$ is unitary because $U^\dagger\circ U=U\circ U^\dagger=I$ $\endgroup$
    – Piquito
    Jan 10, 2016 at 22:43

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Hermitian is because Charles Hermite. List of things named after Charles Hermite. Unitary is because it is an extension of the concept of unit complex number.

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    $\begingroup$ Also for "first appearences" there's a great website (jeff560.tripod.com/h.html, e.g. lists "Hermitian Matrix") $\endgroup$ Jan 10, 2016 at 22:37
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    $\begingroup$ Bad idea to name it after Hermite! I would call it adjoint-invariant ! $\endgroup$
    – Rescy_
    Jan 10, 2016 at 22:38
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    $\begingroup$ @MaximilianGerhardt Thank you so much! $\endgroup$
    – Rescy_
    Jan 10, 2016 at 22:39
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    $\begingroup$ @Rescy_ The usage is that things often take names after the people that studied them first... whether other names would be clearer or not. (The worst example I know of is Poisson Binomial Distributions and Poisson distributions, that share a name but are not related at all...) $\endgroup$
    – Clement C.
    Jan 10, 2016 at 22:40
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    $\begingroup$ And how should be named a diophantine equation? the Hamiltonian? the Lagrangian, wronskian? A Riemannian manifold? How should I be named myself? :o) $\endgroup$
    – Bernard
    Jan 10, 2016 at 22:41

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