unitary matrices
Elementary proofs of two theorems involving arguments of eigenvalues of a product of two unitary matrices
... We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices–one by Childs et al. [J. Mod. Phys. 47, 155 (2000)] and the other ...
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The Genetic Coding System and Unitary Matrices
... sparse unitary matrices that are algebraic complementary to each other (they are mirror-anti-symmetric to each other by analogy with the left and right halves of a human body) and that can be considered as ...
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A note on the tensor product of two random unitary matrices
... In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m × m and n × n . When n becomes large, the process behaves like the ...
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On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices
... Now if one considers a finite number of such L-functions, all satisfying the same func- tional equation, then one can wonder if the zeros of a linear combination of these L- functions are still on the critical line. In ...
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Secular determinants of random unitary matrices
... Even though the formula (24) for the variance is primarily meant to cover the four canonical ensembles β = 0 (CPE), 1 (COE), 2 (CUE), and 4 (CSE), we could not resist the temptation to test its usefulness for ...
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Equivalent Conditions on Conjugate Unitary Matrices
... conjugate unitary matrices are ...conjugate unitary matrices are ...secondary unitary matrices, hermitian, s-hermitian and involutary are also ...
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Kronecker product of conjugate unitary matrices
... of matrices is recapitulated using a notation that reveals the tensor structures of the matrices ...of unitary matrices to be developed from a single recursion formula ...
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Mixed moments of characteristic polynomials of random unitary matrices
... A BSTRACT . Following the work of Conrey, Rubinstein and Snaith [11] and Forrester and Witte [16] we ex- amine a mixed moment of the characteristic polynomial and its derivative for matrices from the ...
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Lowener, Star and " " Partial Ordering of S-Unitary Matrices
... Some characterizations of the star partial ordering and rank subtractivity for matrices was discussed by Hartwig and Styan in 3. Jurgen Grob observed some remarks on partial ordering of Hermitian ...
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On unitary bimatrices
... types. Unitary matrices are a firsthand tool in solving many problems in mathematical and theoretical physics and the diversity of the problems necessitates to keep improving ...real matrices, ...
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From a reversible code to the quantum one: R-matrix
... Abstract. This research has been carried out in collaboration with D.Melnikov, A.Mironov, A.Morozov and An.Morozov. We study the relation between quantum pro- gramming and knot theory. The general idea is that knot ...
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Complex Unitary Recurrent Neural Networks Using Scaled Cayley Transform
... a unitary recurrent weight matrix. The unitary evo- lution RNN (uRNN) architecture proposed by (Arjovsky, Shah, and Bengio 2016) maintains a unitary matrix by us- ing a product of simple ...
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Vol 9, No 4 (2018)
... Left star and Right star partial ordering of conjugate unitary matrix was defined and theorems related to left star and right star partial ordering of conjugate unitary matrices are de[r] ...
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Blind Separation of Nonstationary Sources Based on Spatial Time-Frequency Distributions
... Another important contribution of this paper is to pro- pose a new method for selecting autoterm t-f points. Au- toterm point selection is key in maintaining the diagonal structure of the source TFD matrix which is the ...
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Large N expansion for the time delay matrix of ballistic chaotic cavities
... (GUE) matrices are integers and they are related to a very precise enumer- ation ...Wishart matrices. The salient feature of Gaussian and Wishart matrices, and the one which is fundamental for ...
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The structure of doubly non-commuting isometries
... Although there is no mathematical gain for n = 1 by retrieving a decomposi- tion that was used as a key ingredient for the general result to begin with, and a classification result that could have been cited from the ...
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THE THEORY OF REPRESENTATIONS OF GROUPS SO0(2; 1) AND ISO(2; 1). WIGNER COEFFICIENTS OF THE GROUP SO0(2; 1)
... Abstract. This paper is devoted to the representations of the groups SO(2, 1) and ISO(2, 1). Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible ...
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On improvements of Fischer’s inequality and Hadamard’s inequality for K0 matrices
... All matrices considered in this paper are real. For an n × n matrix A, α, β ⊆ n = {, , . . . , n}, the submatrix of A lying in rows indexed by α and the columns indexed by β will be denoted by A[α, β ]. If α = ...
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Inter relations between cognitive factors in the prediction of outcome among chronic alcoholics
... THE BROAD PERSPECTIVE The Extent of Problem Drinking Developments in Alcoholism Research Changing Attitudes Towards Alcohol Abuse The Unitary Model of Alcoholism Criticism of the Unitary[r] ...
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The structure and the number of $P 7$ free bipartite graphs
... by Alekseev in [2]. Moreover, Alekseev described the set of minimal classes in all the four lower layers and the asymptotic structure of properties in the first three of them. A more detailed description of the ...
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