منابع مشابه
Unitary Matrices and Hermitian Matrices
Unitary Matrices and Hermitian Matrices Recall that the conjugate of a complex number a + bi is a − bi. The conjugate of a + bi is denoted a+ bi or (a+ bi)∗. In this section, I’ll use ( ) for complex conjugation of numbers of matrices. I want to use ( )∗ to denote an operation on matrices, the conjugate transpose. Thus, 3 + 4i = 3− 4i, 5− 6i = 5 + 6i, 7i = −7i, 10 = 10. Complex conjugation sati...
متن کاملHaar-Distributed Unitary Matrices
We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random n × n unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) k × k submatrix converges in distribution, after multiplying by a normalization factor √ n and as n → ∞, to a matrix of independent complex Gaussian random variables with mean 0...
متن کاملGraphs of unitary matrices
The support of a matrix M is the (0, 1)-matrix with ij-th entry equal to 1 if the ij-th entry of M is non-zero, and equal to 0, otherwise. The digraph whose adjacency matrix is the support of M is said to be the digraph of M . This paper observes some structural properties of digraphs and Cayley digraphs, of unitary matrices. We prove that a group generated by two elements has a set of generato...
متن کاملUnitary rank structured matrices
In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of unitary or Givens transformations. We provide also some basic operations for manipulating the representation, such as the transition to zerocreating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of ...
متن کاملTruncations of random unitary matrices
We analyse properties of non-Hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N > M , distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1989
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(16)30305-6