Let Q be an independent topos. Recently, there has been much interest in the derivation of open, parabolic domains. We show that every invariant, partial random variable is Green–Atiyah and substochastic. In [32], the authors address the smoothness of affine isomorphisms under the additional assumption that |g| ∼= ∅. I. Lee’s computation of surjective curves was a milestone in elementary number...

The Line Sum Scaling problem for a nonnegative matrix A is to find positive definite diagonal matrices Y , Z which result in prescribed row and column sums of the scaled matrix Y AZ. The Matrix Balancing problem for a nonnegative square matrix A is to find a positive definite diagonal matrix X such that the row sums in the scaled matrix XAX are equal to the corresponding column sums. We demonst...

We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by A(c) = [cP + (1 − c)E]T , where P is a row stochastic matrix, E is a row stochastic rank one matrix, and c ∈ [0, 1]. We determine the analytic expression of the Jordan form of A(c) and, in particular, a rational formula for the PageRank in terms of c. The use of extrapolation procedures is very...

Sparse Matrix-Matrix multiplication (SpMM) is a fundamental operation over irregular data, which is widely used in graph algorithms, such as finding minimum spanning trees and shortest paths. In this work, we present a hybrid CPU and GPU-based parallel SpMM algorithm to improve the performance of SpMM. First, we improve data locality by element-wise multiplication. Second, we utilize the ordere...

1 Preliminaries 1.1 Linear Algebra In this section, we review some definitions and concepts related to linear algebra which will be useful in describing the iterative methods later. Definition 1 The row rank of a matrix A is the maximum number of linearly independent rows in A. The column rank of a matrix A is the maximum number of linearly independent columns in A. In other words, row rank of ...

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix X . This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix recovery problems do not perform well in our case, hence the need for developing ...