Matrix balancing is a term that describes the process of altering the elements of a matrix to make it conform to known regularity conditions while still remaining close to the original matrix Often the regularity conditions relate only to the row and col umn sums which yields problems having a desirable network structure We describe an application in telecommunication demand forecasting that ad...

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 ...

1. Let A be an n× n matrix with complex coefficients. Define trA to be the sum of the diagonal elements. Show that trA is invariant under conjugation, i.e., trA = trPAP for all invertible n× n matrices P. Proof. Let P be an invertible matrix. Let ~pk be the k-th row of P, ~qj the j-th column of P, and ~ ai the i-th column of A. The k-th row of the matrix PA is 〈~pk · ~ a1, . . . ,~pk · ~ an〉. S...

A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no...