Hermitian matrix

English

Alternative forms

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Etymology

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

Pronunciation

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Noun

1. Template:Lb A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that $A=A^{†}.$

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   • 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).

   • 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 hermitian matrix, exp(iH) is a unitary matrix. The converse is also true, i.e., if U is any unitary matrix, then it can be expressed in the form

     U = exp(iH),          (4.94)

     where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix.

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Hypernyms

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Hyponyms

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• Template:L matrix
• Template:L, Template:L matrix

Translations

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• Finnish: Template:T
• Icelandic: Template:T, Template:T
• Italian: Template:T
• Polish: Template:T
• Russian: Template:T, Template:T

References

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