The first thing taught in Math 340 is Gaussian Elimination, i.e. the process of transforming a matrix to reduced row echelon form by elementary row operations. Because this process has the effect of multiplying the matrix by an invertible matrix it has produces a new matrix for which the solution space of the corresponding linear system is unchanged. This is made precise by Theorem 2.4 below. T...

This chapter introduces a variety of tools from matrix algebra and multivariate statistics useful in the analysis of selection on multiple characters. Our primary intent is to introduce the reader to the idea of vectors and matrices as geometric structures, viewing matrix operations as transformations converting a vector into a new vector by a change in geometry (rotation and scaling). The eige...

We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time.

Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations. Calculations can, therefore, be performed in a fully parallel manner. Several different optical methods for performing residue arithmetic operations are described. A possible combination of such methods to form a matrix vector multipl...

Let A 2 R mn be a matrix with known singular values and singular vectors, and let A 0 be the matrix obtained by appending a row to A. We present stable and fast algorithms for computing the singular values and the singular vectors of A 0 in O ? (m + n) min(m;n) log 2 2 oating point operations, where is the machine precision. Previous algorithms can be unstable and compute the singular values an...

In this paper we have introduced the concept of intuitionistic fuzzy soft matrix and defined different types of matrices along with some new operations in the parlance of intuitionistic fuzzy soft set theory. Then based on some of these new matrix operations a new efficient methodology named as IFSM -Algorithm has been developed to solve intuitionistic fuzzy soft set based group decision making...

In this paper we propose design of three systolic arrays to perform QR decomposition of a square matrix. Our first design is based on Given’s rotation method [1]. In contrast to the earlier designs [1], [2] based on this method, our design uses n(n − 1)/2 homogeneous PEs. Our next design is based on Householder method [4]. This method performs only (n− 1) square root operations in contrast to n...

A distributed algorithm with the same functionality as the single-processor level 3 BLAS operation GEMM, i.e., general matrix multiply and add, is presented. With the same functionality we mean the ability to perform GEMM operations on arbitrary subarrays of the matrices involved. The logical network is a 2D square mesh with torus connec-tivity. The matrices involved are distributed with non-sc...

The records of superior performance of selected service firms over many years suggest that they may be more productive than others. This article uses the Theory of Swift, Even Flow to explain why that might be true. In the process, this article improves Schmenner’s 1986 service process matrix. The redefinition of the axes of this matrix and of the resulting diagonal leads to enhanced understand...

Gaussian processes (GPs) provide a flexible framework for probabilistic regression. The necessary computations involve standard matrix operations. There have been several attempts to accelerate these operations based on fast kernel matrix-vector multiplications. By focussing on the simplest GP computation, corresponding to test-time predictions in kernel ridge regression, we conclude that simpl...