scholarly journals Linearization of Poisson actions and singular values of matrix products

2001 ◽  
Vol 51 (6) ◽  
pp. 1691-1717 ◽  
Author(s):  
Anton Alekseev ◽  
Eckhard Meinrenken ◽  
Chris Woodward
Keyword(s):  
Singular Values ◽  
Matrix Products ◽  
Poisson Actions

scholarly journals Random matrix products: Universality and least singular values

2020 ◽  
Vol 48 (3) ◽  
pp. 1372-1410
Author(s):  
Phil Kopel ◽  
Sean O’Rourke ◽  
Van Vu
Keyword(s):  
Random Matrix ◽  
Singular Values ◽  
Random Matrix Products ◽  
Matrix Products

scholarly journals Non-asymptotic Results for Singular Values of Gaussian Matrix Products

2021 ◽  
Author(s):  
Boris Hanin ◽  
Grigoris Paouris
Keyword(s):  
Singular Values ◽  
Asymptotic Results ◽  
Matrix Products

scholarly journals On the Kronecker Products and Their Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Huamin Zhang ◽  
Feng Ding
Keyword(s):  
Kronecker Product ◽  
Polynomial Matrix ◽  
Singular Values ◽  
Permutation Matrix ◽  
Kronecker Products ◽  
Mixed Matrix ◽  
Matrix Products ◽  
Vector Operator

This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.

scholarly journals A note on invariance of the eigenvalues, singular values, and norms of matrix products involving generalized inverses

1992 ◽  
Vol 165 ◽  
pp. 125-130 ◽  
Author(s):  
Jerzy K. Baksalary ◽  
Tarmo Pukkila
Keyword(s):  
Singular Values ◽  
Generalized Inverses ◽  
Matrix Products

scholarly journals Universality and least singular values of random matrix products: A simplified approach

Bernoulli ◽  
2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Rohit Chaudhuri ◽  
Vishesh Jain ◽  
Natesh S. Pillai
Keyword(s):  
Random Matrix ◽  
Singular Values ◽  
Simplified Approach ◽  
Random Matrix Products ◽  
Matrix Products

scholarly journals Some inequalities for singular values of matrix products

1997 ◽  
Vol 264 ◽  
pp. 109-115 ◽  
Author(s):  
Bo-Ying Wang ◽  
Bo-Yan Xi
Keyword(s):  
Singular Values ◽  
Matrix Products

A SVD and Modified Firefly Optimization Based Robust Digital Image Watermarking Technique

2017 ◽  
Vol 7 (7) ◽  
pp. 268
Author(s):  
Chauhan Usha ◽  
Singh Rajeev Kumar
Keyword(s):  
Digital Media ◽  
Firefly Algorithm ◽  
Image Watermarking ◽  
Singular Values ◽  
Robust Watermarking ◽  
Scaling Factors ◽  
Geometric Attacks ◽  
Host Image ◽  
Firefly Optimization ◽  
Value Decomposition

Digital Watermarking is a technology, to facilitate the authentication, copyright protection and Security of digital media. The objective of developing a robust watermarking technique is to incorporate the maximum possible robustness without compromising with the transparency. Singular Value Decomposition (SVD) using Firefly Algorithm provides this objective of an optimal robust watermarking technique. Multiple scaling factors are used to embed the watermark image into the host by multiplying these scaling factors with the Singular Values (SV) of the host image. Firefly Algorithm is used to optimize the modified host image to achieve the highest possible robustness and transparency. This approach can significantly increase the quality of watermarked image and provide more robustness to the embedded watermark against various attacks such as noise, geometric attacks, filtering attacks etc.

Estimation of the Number of Signal Components Based on Singular Values of Noise Subspace

2011 ◽  
Vol 33 (9) ◽  
pp. 2039-2044 ◽  
Author(s):  
Xin-peng Zhou ◽  
Feng Han ◽  
Guo-hua Wei ◽  
Si-liang Wu
Keyword(s):  
Singular Values ◽  
Noise Subspace

Analysis of multiplicity of Hankel singular values of control systems

2015 ◽  
Vol 76 (2) ◽  
pp. 205-218 ◽  
Author(s):  
L. A. Mironovskii ◽  
T. N. Solov’eva
Keyword(s):  
Control Systems ◽  
Singular Values ◽  
Hankel Singular Values

scholarly journals Ramanujan’s function k(τ)=r(τ)r 2(2τ) and its modularity

2020 ◽  
Vol 18 (1) ◽  
pp. 1727-1741
Author(s):  
Yoonjin Lee ◽  
Yoon Kyung Park
Keyword(s):  
Continued Fraction ◽  
Quadratic Field ◽  
Singular Values ◽  
Modular Function ◽  
Imaginary Quadratic Field ◽  
Modular Equations ◽  
Positive Rational Number ◽  
Congruence Relations ◽  
Symmetry Relations ◽  
Ray Class Field

Abstract We study the modularity of Ramanujan’s function k ( τ ) = r ( τ ) r 2 ( 2 τ ) k(\tau )=r(\tau ){r}^{2}(2\tau ) , where r ( τ ) r(\tau ) is the Rogers-Ramanujan continued fraction. We first find the modular equation of k ( τ ) k(\tau ) of “an” level, and we obtain some symmetry relations and some congruence relations which are satisfied by the modular equations; these relations are quite useful for reduction of the computation cost for finding the modular equations. We also show that for some τ \tau in an imaginary quadratic field, the value k ( τ ) k(\tau ) generates the ray class field over an imaginary quadratic field modulo 10; this is because the function k is a generator of the field of the modular function on Γ 1 ( 10 ) {{\mathrm{\Gamma}}}_{1}(10) . Furthermore, we suggest a rather optimal way of evaluating the singular values of k ( τ ) k(\tau ) using the modular equations in the following two ways: one is that if j ( τ ) j(\tau ) is the elliptic modular function, then one can explicitly evaluate the value k ( τ ) k(\tau ) , and the other is that once the value k ( τ ) k(\tau ) is given, we can obtain the value k ( r τ ) k(r\tau ) for any positive rational number r immediately.

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