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Glite Dictionary
Hermitian

Hermitian

1 9.9
A matrix or operator equal to its own conjugate transpose
  • adjective
  • /hɜrˈmɪʃən/
  • Specialized
: hermitiano
  • Which describes the stochastic evolution of eigenvalues of a Hermitian matrix under independent Brownian motion of its entries and is discussed in this previous blog post.

In other words, the eigenvectors of Hermitian matrices define a basis.

Examples

  • In other words, the eigenvectors of Hermitian matrices define a basis.

    Stanford

  • They're perhaps the as important as the Hermitian operators, if not more.

  • Now, we probably have heard that Hermitian operators do the job.

  • So this is the notion of a Hermitian matrix.

  • For every quantum state and every Hermitian operator, the math of QM allows you to calculate tr D.

    Blog text (29)

  • At every instant of time, the density matrix is always a Hermitian, positive-definite, trace-one matrix, so you can always diagonalize it, and its eigenvalues are always real, positive, and sum to one.

    Blog text (29)

  • This led to the discovery of one of the most beautifully symmetric structures—the Albert algebra of 3 x 3 Hermitian matrices of octonions.

    Academic text (1999)

  • The states are orthogonal whenever they're different-eigenvalue eigenstates of a Hermitian operator, e.g., Jz in this case; it's a trivial one-line proof in linear algebra.

    Blog text (30)

  • A Hermitian matrix is one that is equal to its own conjugate transpose.

  • In quantum mechanics, measurements are often represented by Hermitian operators.

Surface Forms

Hermitian positive

Morphology

Hermitian = Hermite (semi-transparent) = Hermite + ian

The adjective is formed regularly by adding -ian to the proper name Hermite, but the meaning is a specialized eponym referring to mathematical objects and is not inferable by learners who do not know the name.

Etymology

The word Hermitian is named after the French mathematician Hermite and the ending -ian means 'related to' or 'belonging to', just like in Newtonian. So a Hermitian matrix or operator has a special mirror symmetry named for Hermite, and that is why these objects have real important numbers called eigenvalues.