See Hermitian matrix in All languages combined, or Wiktionary
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"etymology_text": "Named after French mathematician Charles Hermite (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues.",
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"text": "Hermitian matrices have real diagonal elements as well as real eigenvalues.",
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"text": "If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal.",
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"text": "If an observable can be described by a Hermitian matrix H, then for a given state #x5C;langleA#x5C;rangle, the expectation value of the observable for that state is #x5C;langleA#x7C;H#x7C;A#x5C;rangle.",
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"text": "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,\nThere 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)."
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"ref": "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)",
"text": "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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"ref": "1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:",
"text": "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.",
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"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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"(linear algebra) 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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"word": "hermitovská matice"
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"text": "If an observable can be described by a Hermitian matrix H, then for a given state #x5C;langleA#x5C;rangle, the expectation value of the observable for that state is #x5C;langleA#x7C;H#x7C;A#x5C;rangle.",
"type": "example"
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"text": "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,\nThere 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)."
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"ref": "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)",
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},
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"ref": "1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:",
"text": "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.",
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"(linear algebra) 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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"word": "hermitovská matice"
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"sense": "square matrix equal to its own conjugate transpose",
"tags": [
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"word": "matrice hermitiana"
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"sense": "square matrix equal to its own conjugate transpose",
"tags": [
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"word": "macierz hermitowska"
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"roman": "ermítova mátrica",
"sense": "square matrix equal to its own conjugate transpose",
"tags": [
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"word": "эрми́това ма́трица"
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