On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices
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DOI: 10.1007/s00440-021-01101-0
Abstract: Let $U^N = (U_1^N,\dots, U^N_p)$ be a d-tuple of $N\times N$ independent Haar unitary matrices and $Z^{NM}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otimes \mathbb{M}_M(\mathbb{C})$. Let $P$ be a self-adjoint non-commutative polynomial. In 1998,… read more here.
Keywords: haar unitary; unitary matrices; almost surely; deterministic matrices ... See more keywords
Congruence of Unitary Matrices
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DOI: 10.1007/s10958-021-05369-4
Abstract: C. R. Johnson and S. Furtado have shown that if two unitary matrices are *-congruent, then they are unitarily similar. A counterpart of this statement concerning another type of matrix congruence, namely, the T-congruence is… read more here.
Keywords: congruence; congruence unitary; unitary matrices;
The Birkhoff theorem for unitary matrices of arbitrary dimensions
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DOI: 10.1016/j.laa.2016.10.028
Abstract: Abstract It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of… read more here.
Keywords: arbitrary dimensions; matrices arbitrary; birkhoff theorem; unitary matrices ... See more keywords
A note on factoring unitary matrices
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DOI: 10.1016/j.laa.2018.02.017
Abstract: Abstract The note concerns three factorizations of unitary matrices: a recent factorization allowing to obtain any unitary matrix of dimension 2n from four unitary matrices of dimension n; the Cosine–Sine decomposition; and a new factorization… read more here.
Keywords: note factoring; factoring unitary; unitary matrix; unitary matrices ... See more keywords
Level Compressibility of Certain Random Unitary Matrices
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DOI: 10.3390/e24060795
Abstract: The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing… read more here.
Keywords: compressibility certain; level compressibility; unitary matrices; random unitary ... See more keywords