What is the origin of the name Hermitian and Unitary matrix?

Question

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

My question is:

Why do we name matrices of such properties Hermitian and Unitary? These names are non-intuitive and have nothing to do with these properties.
Who named them?
Possible citation of first appearance in paper?

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

AHusain · Accepted Answer · 2016-01-10 22:36:07Z

6

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.

answered Jan 10, 2016 at 22:36

AHusain

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$\begingroup$ Also for "first appearences" there's a great website (jeff560.tripod.com/h.html, e.g. lists "Hermitian Matrix") $\endgroup$
– Maximilian Gerhardt
Commented 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_
Commented Jan 10, 2016 at 22:38
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$\begingroup$ @MaximilianGerhardt Thank you so much! $\endgroup$
– Rescy_
Commented 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.
Commented 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
Commented Jan 10, 2016 at 22:41

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