, n, and let ‖‖ denote the spectral norm. In a previous paper it was proved that Here we prove that Each inequality implies, and is equivalent to, the triangle inequality for the recently constructed spherical distance of a projective matrix space, and the validity of either of these ...
If Ais the original matrix is the matrix with entries replaced, and are the values of the spectral norm on Aand , respectively, then it is easy to show that . In this paper we place this question in a slightly more general setting and for complex matrices we characterize the case of ...
We show that if b tends to infinity faster than the third power of log N, then the spectral norm is bounded with probability 1.A. KhorunzhyMathematicsA. Khorunzhy, "On spectral norm of large band random matrices," preprint, Apr. 2004....
We show that for n3 the class of these matrices contains the normal matrices as a subclass.doi:10.1016/0024-3795(74)90076-7M.GoldbergandG.ZwasElsevier Inc.Linear Algebra and its ApplicationsM. Goldberg, G. Zwas, On matrices having equal spectral radius and spectral norm, Linear Algebra ...
The literature presents several estimates for this condition number with varying results; even standard reference texts contain serious overestimates. The use of the nuclear norm affords a single derivation of the best known lower and upper bounds on the condition number and shows why there is ...
To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spectral norm regularization, which penalizes the high spectral norm of weight matrices in neural networks. We provide supportive evidence for the abovementioned hypothesis by experimentally ...
0 - This is a modal window. No compatible source was found for this media. numpynpscipylinalgnorm# Define the zero matrixA=np.zeros((2,2))# Compute the L2 norm (spectral norm)l2_norm=norm(A,ord=2)print("Zero Matrix A:")print(A)print("L2 Norm (Spectral Norm) of A:",l2_norm...
I wonder if the 2-norm or spectral norm is also submultiplicative for non-squared matrices, i.e.∥AB∥2≤∥A∥2⋅∥B∥2‖AB‖2≤‖A‖2⋅‖B‖2if the number of columns of A coincides with the number of rows of B. In the literature I can only find a statement about square ...
[1] established bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erdös-Rényi graphs. Hu et al. [20] studied the largest eigenvalue and the spectral norm of the Hermitian adjacency matrix of random mixed graphs....
The overall presentation of the matrix-less paradigm is carried out for the first time in a systematic way and in full generality for arbitrary sequences of structured matrices, including (but not limited to) GLT sequences. The present work can hence be considered as a review and a generaliza...