Word.ws English Dictionary

Hermitian matrix

US/hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/

Hermitian matrix noun: a square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A=A^†.

Noun

Hermitian matrix (plural Hermitian matrixes or Hermitian matrices)

  1. A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A=A^†.
    • Hermitian matrices have real diagonal elements as well as real eigenvalues.
    • If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal.

Examples of Hermitian matrix in a sentence

  • If an observable can be described by a Hermitian matrix H, then for a given state #92;langleA#92;rangle, the expectation value of the observable for that state is #92;langleA#124;H#124;A#92;rangle.
  • Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix.1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129, For this we note that if H is a...

Forms of Hermitian matrix

pluralHermitian matrixes
pluralHermitian matrices
alternative formhermitian matrix

Origin of Hermitian matrix

Named after French mathematician Charles Hermite (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues.

Questions about Hermitian matrix

What does Hermitian matrix mean?
Hermitian matrix means a square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A=A^†.
How do you use Hermitian matrix in a sentence?
If an observable can be described by a Hermitian matrix H, then for a given state #92;langleA#92;rangle, the expectation value of the observable for that state is #92;langleA#124;H#124;A#92;rangle.
What part of speech is Hermitian matrix?
Hermitian matrix is a noun.
How do you pronounce Hermitian matrix?
Hermitian matrix is pronounced /hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/ (US).
What is the plural of Hermitian matrix?
The plural of Hermitian matrix is Hermitian matrixes.

Words near Hermitian matrix in the dictionary

  1. hermithood
  2. hermitian
  3. Hermitian conjugate
  4. Hermitian conjugates
  5. Hermitian matrices
  6. Hermitian matrix
  7. Hermitians
  8. hermitic
  9. hermitical
  10. hermitically
  11. hermiticity

Source and license

Adapted from Wiktionary: Hermitian matrix (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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