In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling.

Let Sn(S) denote the set of symmetric matrices over some semiring, S. A line of A ∈ Sn(S) is a row or a column of A. A star of A is the submatrix of A consisting of a row and the corresponding column of A. The term rank of A is the minimum number of lines that contain all the nonzero entries of A. The star cover number is the minimum number of stars that contain all the nonzero entries of A. Th...

The evolution of genetic systems has been analyzed through the use of modifier gene models, in which a neutral gene is posited to control the transmission of other genes under selection. Analysis of modifier gene models has found the manifestations of an "evolutionary reduction principle": in a population near equilibrium, a new modifier allele that scales equally all transition probabilities b...

with Application to Gene-Expression Analysis Sepp Hochreiter [email protected] Klaus Obermayer Fakultät für Elektrotechnik und Informatik Technische Universität Berlin Franklinstr. 28/29, 10587 Berlin, Germany [email protected] We consider the classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects where row and column ...

The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation f x g x ∫∞ 0 k x − t f t dt ∫0 −∞ T x − t f t dt, where K, T are n × n matrix valued functions, n ≥ 1, with nonnegative integrable elements, are considered in one semiconservative singular case, where the matrix A ∫∞ −∞ K x dx is stochastic one and the matrix B ∫∞ −∞ T x dx is substochasti...

Some large rectangular matrices used in animal breeding are presented. We describe how to generate these matrices from the data supplied by animal breeders. The matrices are very sparse (3 nonzeros per row) and range between 26 20 and 968 652 582 694.

A square matrix is called line-sum-symmetric if the sum of elements in each of its rows equals the sum of elements in the corresponding column. Let A be an n x n nonnegative matrix and let X and Y be n x n diagonal matrices having positive diagonal elements. Then the matrices XA, XAXand XA Yare called a row-scaling, a similarity-scaling and an equivalence-scaling of A. The purpose of this paper...

A two player game (or more correctly, a two player normal-form game) is specified by two m × n payoff matrices R and C corresponding to the row and column player respectively. Each of these matrices has m rows corresponding to the m strategies of the row player and n columns corresponding to the n strategies of the column payer. The row player picks a row i ∈ [m], and the column player picks a ...

We prove that perceptrons separating Boolean matrices in which each row has a one from matrices in which many rows have no one must have either large total weight or large order. This result extends one-in-a-box theorem by Minsky and Papert 13] stating that perceptrons of small order cannot decide if each row of a given Boolean matrix has a one. As a consequence, we prove that AM \ co-AM 6 6 PP...