1), Hermitian (=2), and Hermitian self-dual (=4) random matrix models with rank 1 external source. They are analyzed in a uniform way by a contour integral representation of the joint probability density function of eigenvalues. Assuming the "one-band" condition and certain regularities of ...
In this paper we prove that the ring R=Z8[X]/ is a local ring with unique maximal ideal, thereby implying that R is not a principal ideal ring. We also prove that cyclic codes of length 2k over Z8 are generated as ideals by at most three elements....
The Largest Eigenvalue of Real Symmetric, Hermitian and Hermitian Self-dual Random Matrix Models with Rank One External Source, Part I 1), Hermitian (=2), and Hermitian self-dual (=4) random matrix models with rank 1 external source. They are analyzed in a uniform way by a contour integr...
In matrix notation, the transformation is written as: [2.33][Y]=[A][X] In the terminology of linear operators, [a*] T is known as the adjoint matrix of [A] and matrices [H] or [S] are said to be self-adjoint. Going a little bit further, the vector space can be provided ...
A self-adjoint operator has a Hermitian matrix representation in which the Hermitian matrix is equal to the complex conjugate of its transpose in which the matrix rows and columns are exchanged. The Hermitian matrix representation of A^, the conjugate transpose, is (90)A^+=A^T∗. The matri...
. It is convenient to introduce a self-dual orthonormal basis |n , where x|n = P n (x)/ √ h n , and |x are eigenvectors of the operator ˆ φ with eigenvalues x, satisfying the normalization x ′ |x = exp(NV (x)) δ(x ′ ...
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Random matrixQuaternion self-dual Hermitian matricesIn this paper, convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices are investigated. We show that under conditions of finite 6th moments, the expected spectral......
Random matrixQuaternion self-dual Hermitian matricesIn this paper, convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices are investigated. We show that under conditions of finite 6th moments, the expected spectral distribution of a large quaternion self-dual Hermitian ...
Circulant matrixIsodual codeIn this paper, we investigate free Hermitian self-dual codes whose generator matrices are of the form [I,A+vB] over the ring F2+vF2={0,1,v,1+v} with v2=v. We use the double-circulant, the bordered double-circulant and the symmetric construction methods to ...