Let El be a blog and Aεℳnn a square matrix. We say that A is right or left column-regular if the columns of A are right or left SLI respectively. And we make corresponding dual definitions in the obvious way.Page %P Close Plain text Look Inside Other actions Export citation ...
Low-Rank Matrix Completion 低阶矩阵完备.pdf,Matrices URT Matrices Z such that of rank k P⌦ (Z) = P⌦ (M ) T 2 URT kUR Z kF Z 0 0 10 10 −2 −2 10 10 E E S S M 10−4 M 10−4 R R e e v v i −6 i −6 t t a 10 a 10 l l e e R R −8...
Moore-Penrose generalized inverse of a rectangular matrix. In Kalaba et al. [3] we show how Decell's algorithm, given by a finite sequence of matrices and scalars to be computed recursively, can be useful in the development of the algebraic properties of the Moore...
Tensor rank is not a straight-forward extension of matrix rank. A constructive proof based on an eigenvalue criterion is provided that shows when a 2 × 2 × 2 tensor over ℝ is rank-3 and when it is rank-2. The results are extended to show that n × n × 2 ...
Define the weight of a matrix to be the number of non-zero entries. One would like to count $m$ by $n$ matrices over a finite field by their weight and rank. This is equivalent to determining the probability distribution of the weight while conditioning on the rank. The complete answer...
We review some recent approaches to robust approximations of low-rank data matrices. We consider the problem of estimating a low-rank mean matrix when the data matrix is subject to measurement errors as well as gross outliers in some of its entries. The purpose of the paper is to make vario...
However, it does not allow an explicit control on the rank of W . That is, the non-zero singular values of matrix W will change along with W ∗, but the rank of W may remain unchanged. In this sense, trace norm may not be a good surrogate to obtain the minimal rank matrix. ...
Dynamical low-rank integrators for matrix differential equations recently attracted a lot of attention and have proven to be very efficient in various appl
Low-Rank Matrix Completion is an important problem with several applications in areas such as recommendation systems, sketching, and quantum tomography. The goal in matrix completion is to recover a low rank matrix, given a small number of entries of the matrix. Source: [Universal Matrix ...
The problem of choosing the missing entry in the partial matrix \(\begin{bmatrix}\text{A} & \text{C} \\\text{B} & ? \end{bmatrix}\) so as to minimize the rank, which had earlier been solved only under a somewhat restrictive hypothesis, is here given a general solution, with desc...