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- W2895037401 abstract "Publisher SummaryThis chapter discusses the joint probability density function for eigenvalues. The joint probability density function for the eigenvalues 1,2, …, N can be obtained by expressing the various components of H in terms of the N eigenvalues j and other mutually independent variables, which together with the j form a complete set. To define U completely, the phases of the eigenvectors must be fixed in some way—for instance, by requiring that the first nonvanishing component be positive. In addition to the real eigenvalues, the number of real independent parameters pμ needed to specify an arbitrary Hermitian matrix H completely is N(N – 1). It is possible to understand the different powers of β by a simple mathematical argument based on counting dimensions." @default.
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- W2895037401 date "1967-01-01" @default.
- W2895037401 modified "2023-09-27" @default.
- W2895037401 title "Gaussian Ensembles. The Joint Probability Density Function for the Eigenvalues††This chapter is based largely on Wigner's article [6]." @default.
- W2895037401 doi "https://doi.org/10.1016/b978-1-4832-3258-4.50006-9" @default.
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