Phrase guide

Hermitian matrix

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

  • US: /hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/

1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: linear-algebra, mathematics, sciences

Examples

  • 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.
  • 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.
  • 1988, I. M. Gelfand, M. I. Graev, Geometry of homogeneous spaces, representations of groups in homogeneous spaces and related questions of integral geometry, Israel M. Gelfand, Collected Papers, Volume II, Springer-Verlag, page 366, There are three types of such spaces: the space of positive definite (or negative definite) Hermitian matrices, the space of nondefinite Hermitian matrices, and finally the space of degenerate Hermitian matrices p, satisfying the condition p ≥ 0 (or p ≤ 0).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

8 source translations are retained for this English entry.

  • Czech: hermitovská matice — square matrix equal to its own conjugate transpose
  • Finnish: hermiittinen matriisi — square matrix equal to its own conjugate transpose
  • Icelandic: sjálfoka fylki — square matrix equal to its own conjugate transpose
  • Icelandic: hermískt fylki — square matrix equal to its own conjugate transpose
  • Italian: matrice hermitiana — square matrix equal to its own conjugate transpose
  • Polish: macierz hermitowska — square matrix equal to its own conjugate transpose
  • Russian: эрми́това ма́трица (ermítova mátrica) — square matrix equal to its own conjugate transpose
  • Russian: самосопряжённая ма́трица (samosoprjažónnaja mátrica) — square matrix equal to its own conjugate transpose