hermitian matrix
/hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/
Word Rarity
Very rare
Frequency: Zipf frequency 2.09 in modern English
29
Scrabble Score
15
Letters
5
Syllables
9
Unique Chars
Meaning
noun
A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A=A^†.
Example Sentences
- "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)."
- "where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix."
- "Exploiting the properties of hermitian matrixes [2], it is possible to obtain an analytical expression for the characteristic function of a hermitian quadratic form of gaussian variables, which is useful in the evaluation of transmission system performance."
Etymology
Named after French mathematician Charles Hermite (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues.
Regional Pronunciation
- American English: /hɝˈmɪ.ʃən ˈmeɪ.tɹɪks/
Inflected Forms
Hermitian matrixes (plural)
Hermitian matrices (plural)