Matrix properties In this section, we will look at some of the important properties matrices which are very useful for deep learning applications. Norm: Norm is an important property of a vector or a matrix that measures the size of the vector or the matrix. Geometrically it can also be int...
MATRIX normsNONNEGATIVE matricesMATHEMATICAL proofsESTIMATION theoryWe study properties of the logarithmic matrix norm. We obtain new estimates for matrix norms as well as for the spectral radius and the spectral abscissa. We give a new proof of the Fiedler theorem and a block test for the ...
The second type consists of all possible data variations in a neighbourhood specified by a certain matrix norm; this is related to the tolerance approach to sensitivity analysis, or to stability. The matrix properties discussed in this paper are positive definiteness; P-matrix, H-matrix and P-...
For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}.We show that ry is a generalized matrix norm if and only ifn∑j=1νj≠ 0.Next, we study some properties of the y-numerical radius of matrices andvectors with non-negative entries....
Recently, a nonconvex relaxation of low-rank matrix recovery (LMR), called the Schatten-p quasi-norm minimization (0 < p < 1), was introduced instead of the previous nuclear norm minimization in order to approximate the problem of LMR closer. In this paper, we introduce a notion of the ...
We investigate the properties of the approximate ‖·‖-inverses G of an n + 1 by n real matrix D of rank n using any arbitrary vector norm ·. We give an explicit formula for G, and we formulate the condition on D under which G is unique. The main result is an extension of the...
In this paper we study the properties of the centered (norm of the) gradient squared of the discrete Gaussian free field in,and. The covariance structure of the field is a function of the transfer current matrix and this relates the model to a class of systems (e.g. height-one field of...
2.1.1644 Part 1 Section 22.1.2.9, baseJc (Matrix Base Justification) 2.1.1645 Part 1 Section 22.1.2.11, borderBox (Border-Box Object) 2.1.1646 Part 1 Section 22.1.2.13, box (Box Object) 2.1.1647 Part 1 Section 22.1.2.15, brk (Break) 2.1.1648 Part 1 Section 22.1.2.18,...
The asymptotic properties of the spectrum of non symmetrically perturbed Jacobi matrix sequences Under the mild trace-norm assumptions, we show that the eigenvalues of an arbitrary (non-Hermitian) complex perturbation of a Jacobi matrix sequence (not n... L Golinskii,S Serra-Capizzano - 《...
2.1.1803 Part 4 Section 7.1.2.9, baseJc (Matrix Base Justification) 2.1.1804 Part 4 Section 7.1.2.11, borderBox (Border-Box Function) 2.1.1805 Part 4 Section 7.1.2.13, box (Box Function) 2.1.1806 Part 4 Section 7.1.2.15, brk (Break) 2.1.1807 Part 4 Section 7.1.2.16, brkBin (...