_:b17593799 "1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:"@en . . . _:b17593790 . _:b17593796 "1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:"@en . _:b17593787 "where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix."@en . _:b17593804 "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 \u2265 0 (or p \u2264 0)."@en . _:b7201294 "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"@en . _:b17593792 "where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix."@en . _:b17593804 "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,"@en . _:b17593785 "If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal."@en . _:b7201296 "1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:"@en . _:b17593783 "1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:"@en . _:b7201292 "If an observable can be described by a Hermitian matrix H, then for a given state \\langle A\\rangle, the expectation value of the observable for that state is \\langle A"@en . _:b7201291 "If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal."@en . _:b7201294 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593801 "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"@en . _:b7201295 "where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix."@en . _:b7201295 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593798 "Hermitian matrices have real diagonal elements as well as real eigenvalues."@en . _:b17593803 "H"@en . _:b7201292 "H"@en . _:b17593786 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593787 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . . _:b17593790 "(linear algebra) A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A = A^\\dagger."@en . _:b17593803 "If an observable can be described by a Hermitian matrix H, then for a given state \\langle A\\rangle, the expectation value of the observable for that state is \\langle A"@en . _:b17593796 "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."@en . _:b17593802 . _:b17593803 . _:b17593802 "where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix."@en . _:b17593797 "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,"@en . _:b17593800 . "1" . _:b17593799 "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."@en . _:b17593801 . _:b17593789 "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 \u2265 0 (or p \u2264 0)."@en . _:b17593793 "Hermitian matrices have real diagonal elements as well as real eigenvalues."@en . _:b17593791 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593804 . _:b17593794 . _:b17593795 . . _:b7201296 "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."@en . . _:b17593792 . . _:b17593793 . _:b7201289 "(linear algebra) A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A = A^\\dagger."@en . _:b17593798 . _:b17593784 "Hermitian matrices have real diagonal elements as well as real eigenvalues."@en . _:b17593799 . _:b17593796 . _:b17593797 . _:b17593795 "H"@en . _:b17593800 "If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal."@en . _:b7201290 "Hermitian matrices have real diagonal elements as well as real eigenvalues."@en . _:b17593786 . _:b17593787 . _:b17593795 "If an observable can be described by a Hermitian matrix H, then for a given state \\langle A\\rangle, the expectation value of the observable for that state is \\langle A"@en . _:b17593784 . _:b17593785 . _:b17593801 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593791 . _:b17593788 . _:b17593789 . _:b17593802 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593789 "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,"@en . _:b7201293 "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,"@en . _:b7201293 "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 \u2265 0 (or p \u2264 0)."@en . _:b17593783 . _:b17593783 "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."@en . _:b17593786 "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"@en . _:b17593788 "H"@en . _:b17593794 "If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal."@en . _:b17593806 "(linear algebra) A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A = A^\\dagger."@en . . _:b7201289 . _:b17593805 "(linear algebra) A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A = A^\\dagger."@en . _:b17593797 "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 \u2265 0 (or p \u2264 0)."@en . _:b17593788 "If an observable can be described by a Hermitian matrix H, then for a given state \\langle A\\rangle, the expectation value of the observable for that state is \\langle A"@en . _:b7201296 . _:b17593792 "1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129,"@en . _:b17593791 "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"@en . _:b7201290 . _:b7201291 . _:b17593805 . _:b7201294 . _:b17593806 . _:b7201295 . _:b7201292 . _:b7201293 .