The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
In this paper, one construction of Cartesian authentication codes from the normal form of matrices over finite fields are presented and its size parameters are computed. Moreover, assume that the encoding rules are ch...In this paper, one construction of Cartesian authentication codes from the normal form of matrices over finite fields are presented and its size parameters are computed. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the P I and P S , which denote the largest probabilities of a successful impersonation attack and of a successful substitution attack respectively, of these codes are also computed.展开更多
This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as th...This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.展开更多
Quantum phase transitions (QPTs) play a central role for understanding many-body physics [1]. Different from classical phase transitions which are driven by thermal fluctuations, QPTs are driven by quantum fluctuation...Quantum phase transitions (QPTs) play a central role for understanding many-body physics [1]. Different from classical phase transitions which are driven by thermal fluctuations, QPTs are driven by quantum fluctuations at zero temperature and can be accessed by varying some physical parameters of the many-body system. Characterizing QPTs, which normally needs complicated theoretical calculations, becomes a fundamental problem to further study quantum matters. Here a group of physicists proposed to connect the geometrical properties of reduced density matrices (RDMs) of the physical system with its quantum phase transitions [2,3]展开更多
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
文摘In this paper, one construction of Cartesian authentication codes from the normal form of matrices over finite fields are presented and its size parameters are computed. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the P I and P S , which denote the largest probabilities of a successful impersonation attack and of a successful substitution attack respectively, of these codes are also computed.
文摘This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.
文摘Quantum phase transitions (QPTs) play a central role for understanding many-body physics [1]. Different from classical phase transitions which are driven by thermal fluctuations, QPTs are driven by quantum fluctuations at zero temperature and can be accessed by varying some physical parameters of the many-body system. Characterizing QPTs, which normally needs complicated theoretical calculations, becomes a fundamental problem to further study quantum matters. Here a group of physicists proposed to connect the geometrical properties of reduced density matrices (RDMs) of the physical system with its quantum phase transitions [2,3]
