In this article, we show a "very" simple algorithm for the evaluation of the character tables applicable to all finite point groups. The method uses linear combinations of the symmetry operators associated with the point group's classes as the basis set. Eigenvectors of the resulting matrix of such representations are related to the…

Network meta-analysis has been an essential methodology of systematic reviews for comparative effectiveness research. The restricted maximum likelihood (REML) method is one of the current standard inference methods for multivariate, contrast-based meta-analysis models, but recent studies have revealed the resultant confidence intervals of average…

Before embarking on an individual participant data meta-analysis (IPDMA) project, researchers should consider the power of their planned IPDMA conditional on the studies promising their IPD and their characteristics. Such power estimates help inform whether the IPDMA project is worth the time and funding investment, before IPD are collected. Here,…

Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

The aim of this paper is to describe the innovative teaching approach used in the Southern Federal University, Russia, to teach accounting via a form of matrix mathematics. It thereby contributes to disseminating the technique of teaching to solve accounting cases using mutual calculations to a worldwide audience. The approach taken in this course…

The recent surge of interests in cognitive assessment has led to developments of novel statistical models for diagnostic classification. Central to many such models is the well-known "Q"-matrix, which specifies the item-attribute relationships. This article proposes a data-driven approach to identification of the "Q"-matrix and…

The numerical range, easy to understand but often tedious to compute, provides useful information about a matrix. Here we describe the numerical range of a 3 x 3 magic square. Applying our results to one of the most famous of those squares, the Luoshu, it turns out that its numerical range is a piece of cake--almost.

Two-mode binary data matrices arise in a variety of social network contexts, such as the attendance or non-attendance of individuals at events, the participation or lack of participation of groups in projects, and the votes of judges on cases. A popular method for analyzing such data is two-mode blockmodeling based on structural equivalence, where…

A well known result due to Laplace states the equivalence between two different ways of defining the determinant of a square matrix. We give here a short proof of this result, in a form that can be presented, in our opinion, at any level of undergraduate studies.

A brief history of the development of the empirical equation that is used by prominent, Internet-based programs to estimate (or calculate) the extinction coefficients of proteins is presented. In addition, an overview of a series of related assignments designed to help students understand the origin of the empirical equation is provided. The…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated direct or step-down methods. Here is a short example demonstrating how Excel's sometimes unknown matrix…

We explicitly show that the well-known transmission and reflection amplitudes of planar slabs, obtained via an algebraic summation of Fresnel amplitudes, are completely equivalent to those obtained from transfer matrices in the scattering approach. This equivalence makes the finite periodic systems theory a powerful alternative to the cumbersome…