Results 111 to 120 of about 1,217,124 (142)

THE SPECTRAL NORM OF A CIRCULANT MATRIX

JP Journal of Algebra, Number Theory and Applications, 2018
Summary: Let \(\mathbf{x}=(x_0,\ldots,x_{n-1})\in\mathbb{R}^n\), \(\mathbf{C(x)}\) be the corresponding circulant matrix, and \(\|\cdot\|\) denote the spectral norm. We prove that if the matrix \(\mathbf{C}(\mathbf{x})^T\mathbf{C}(x)\geq \mathbf{O}\) (entrywise), i.e., if \[\begin{aligned} \sum^{n-1}_{i=0}x_i x_{i+j-1}\geq\,\,\text{for all}\,\,j=1 ...
Merikoski, Jorma K., Haukkanen, Pentti, Mattila, Mika, Tossavainen, Timo   +3 more
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Spectral norm of random matrices

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, 2005
This paper studies symmetric random matrices with independent (but not necessarily identical) random variables. It improves an earlier result of \textit{Z.~Füredi} and \textit{J.~Komlós} [Combinatorica 1, 233-241 (1981; Zbl 0494.15010)] on the spectral norm of it. The proof uses Wigner's trace method and a new coding scheme.
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On the Norm and Spectral Radius

Linear and Multilinear Algebra, 1974
(1974). On the Norm and Spectral Radius. Linear and Multilinear Algebra: Vol. 2, No. 3, pp. 239-240.
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On the Spectral Abscissa and the Logarithmic Norm

Mathematical Notes, 2017
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I D Kostrub, A I Perov
exaly   +3 more sources

On the Spectral Norm of Algebraic Numbers

Mathematische Nachrichten, 2003
AbstractIn this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure \documentclass{article} \usepackage{amssymb} \pagestyle{empty} \begin{document} $ \overline {\mathbb Q} $ \end{document} of ℚ in ℂ.
Angel Popescu, Alexandru Zaharescu
exaly   +3 more sources

Spectral norms on valued fields

Mathematische Zeitschrift, 2001
Let \((K,|.|)\) be a perfect valued field, \(\bar{K}\) an algebraic closure of \(K\) and \(|.|\) the extension to \(\bar{K}\). Let \(G\) be the group of all \(K\)-automorphisms of \(\bar{K}\) and \(||x||:= \sup \{|\sigma x|\mid \sigma \in G\}\), the \(G\)-spectral norm on \(\bar K\).
Pasol, Vicentiu, Popescu, Angel, Popescu, Nicolae   +2 more
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On thep-norm joint spectral radius

Journal of Zhejiang University SCIENCE, 2003
The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii.
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Spectral norm of oriented graphs

Linear Algebra and its Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carlos Hoppen, Juan Monsalve, Vilmar Trevisan   +2 more
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Normed Rings and Spectral Representation

1965
A linear space A over a scalar field (F) is said to be an algebra or a ring over (F), if to each pair of elements x, y ∈ A a unique product xy ∈ A is defined with the properties: $$(xy)z = x(yz)(associativity),x(y + z) = xy(distributivity),\alpha \beta (xy) = (\alpha x)(\beta y)$$ (1) If there exists a unit element e such that ex = xe = x for
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Spectral Norm and Nuclear Norm of a Third Order Tensor

Journal of Industrial and Management Optimization, 2022
Liqun Qi, Shenglong Hu
exaly