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A short note on the Frobenius norm of the commutator
Mathematical Notes, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Yan-Dong, Liu, Xu-Qing
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Comments on "Is the Frobenius Matrix Norm Induced?" [with reply]
IEEE Transactions on Automatic Control, 2003In "Is the Frobenius matrix norm induced?", the authors ask whether the Frobenius and the H/sup 2/ norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the H/sup 2/ norm may not be induced. In this paper, it is shown that the Frobenius norm is induced on particular matrix spaces.
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A direct method to Frobenius norm-based matrix regression
International Journal of Computer Mathematics, 2019Regression analysis has been widely used for face recognition. This paper mainly discuss the following regularized matrix regression problem: Given a set of k image matrices A1,A2,…,Ak∈Rm×n and an ...
Shi-Fang Yuan +3 more
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Robust Tensor Completion via Capped Frobenius Norm
IEEE Transactions on Neural Networks and Learning SystemsTensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery ...
Hing Cheung So +2 more
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The Bounds for Spectral Norm and Frobenius Norm Condition Number of a Simple Matrix
2011 Fourth International Conference on Information and Computing, 2011In this paper, we give the estimations both of spectral and Frobenius norm condition number of a simple matrix. The estimations can be used to measure the sensitivity of the solution of linear systems.
Zhiying Ding
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Secure Fingerprint Recognition Based on Frobenius Norm
2012 International Conference on Computer Science and Electronics Engineering, 2012Aiming at the variance of fingerprint feature in multi-capturing and the security of fingerprint template, research on secure fingerprint recognition system based on Frobenius norm is given in this paper. Frobenius norm can show the main information in region of interest (ROI).
Weizhou Zhao, Hui Zhang
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A Logarithmic Minimization Property of the Unitary Polar Factor in the Spectral and Frobenius Norms
SIAM Journal on Matrix Analysis and Applications, 2014The unitary polar factor $Q=U_p$ in the polar decomposition of $Z=U_p \, H$ is the minimizer over unitary matrices $Q$ for both $\|{\rm Log}(Q^* Z)\|^2$ and its Hermitian part $\|{{\rm sym}{_{_*}}\!}({\rm Log}(Q^* Z))\|^2$ over both $\mathbb{R}$ and $\mathbb{C}$ for any given invertible matrix $Z\in\mathbb{C}^{n\times n}$ and any matrix logarithm Log ...
Patrizio Neff +2 more
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Subspace segmentation with a Minimal Squared Frobenius Norm Representation.
2013We introduce a novel subspace segmentation method called Minimal Squared Frobenius Norm Representation (MSFNR). MSFNR performs data clustering by solving a convex optimization problem. We theoretically prove that in the noiseless case, MSFNR is equivalent to the classical Factorization approach and always classifies data correctly.
Yu, Y, Wei, S
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LatLRR for Subspace Clustering via Reweighted Frobenius Norm Minimization
Expert Systems With Applications, 2023Zhi Wang, Tao Jia
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Authors' reply - Comments on "Is the frobenius matrix norm induced?"
IEEE Transactions on Automatic Control, 2003VijaySekhar Chellaboina +1 more
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