A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any…

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…

The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

Students often find their first university linear algebra experience very challenging. While coping with procedural aspects of the subject, solving linear systems and manipulating matrices, they may struggle with crucial conceptual ideas underpinning them, making it very difficult to progress in more advanced courses. This research has sought to…

To examine whether the Roma (Gypsy) population of Serbia, like other South Asian population groups, average lower than Europeans on "g", the general factor of intelligence, we tested 323 16- to 66-year-olds (111 males; 212 females) in three different communities over a two-year-period on the Raven's Colored and/or Standard Progressive…

The paper reports on studies of the impact of harvesting on a prey-predator system with non-monotonic functional response and intra-specific competition in the predator growth dynamics. The existence of its steady states and their stability are studied using eigenvalue analysis. The possibility of the existence of bionomic equilibria has been…

In this paper, formulas for computing the weights that maximize the reliability of a test with multiple parts are derived using a congeneric model. A direct derivation for the three-part test and case and a two-step derivation for the n-part case are presented, and results for these two approaches are shown to be consistent for the three-part…

The use of the 2 x 2 matrix in qualitative data analysis and theory generation is discussed, embracing the perspective that the objective of qualitative research in general and the analysis of qualitative data in particular is the development of theory. A 2 x 2 matrix is considered to be a tabular representation of the relationship of two…

This paper discusses the issue of multiple testing and overall Type I error rates in contexts other than multiple comparisons of means. It demonstrates, using a 5 x 5 correlation matrix, the application of 5 recently developed modified Bonferroni procedures developed by the following authors: (1) Y. Hochberg (1988); (2) B. S. Holland and M. D.…

Either linear or quadratic rules may be used to derive classification equations in discriminant analysis for the purpose of predicting group membership. Generally, the decision about which rule to use is governed by the degree to which the separate group covariance matrices are unequal. An example is presented that supports the superior internal…

Several important issues related to canonical correlation have been recognized and resolved during the last several years. The purpose of this presentation is to offer an organized, comprehensive, and current annotated bibliography of the many recent developments and extensions of canonical methods. The bibliography does not emphasize references…

Provides normative data about the distribution of one measure of similarity of factor loadings, the congruence coefficient, through a Monte Carlo Technique. Matching of "chance" factor patterns was done by the method of Tucker. Statistical tests of the results, based on similarities of the method to canonical and multiple correlation,…

Suggests a way of using factor analytic techniques to supplement multidimensional scaling in such a way as to provide a firm basis for evaluating multidimensional representations. (Author/RC)

Maximum likelihood estimates of the free parameters, and an asymptotic likelihood-ratio test, are given for the hypothesis that one or more elements of a covariance matric are zero, and/or that two or more of its elements are equal. (Author/RC)