Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given…

Although eternally debated, the issue of autonomy in higher education is rarely analysed in its complexity. To address this issue, this article uses an analytical matrix which combines the distinction between substantive and procedural autonomy and the distinction between HEI governing bodies, academic professions and individual academics. This…

This article shows how a matrix can be used to represent a food chain and how the square of this matrix represents the indirect food sources for each animal in the chain. By exploring, through mathematics, the implications when the bottom of the food chain is destroyed, students will see an important connection between mathematics and science.…

The Wechsler Abbreviated Scale of Intelligence (WASI; Psychological Corporation, 1999) and the Wide Range Intelligence Test (WRIT; Glutting, Adams, & Sheslow, 2000) are two well-normed brief measures of general intelligence with subtests purportedly assessing verbal-crystallized abilities and nonverbal-fluid-visual abilities. With a sample of…

As is known, a semi-magic square is an "n x n" matrix having the sum of entries in each row and each column equal to a constant. This note generalizes this notion and introduce a special class of block matrices called "block magic rectangles." It is proved that the Moore-Penrose inverse of a block magic rectangle is also a block magic rectangle.

Issues surrounding student participation, transition, retention and successful completion in higher education are topical. While the Australian federal government has identified broad groupings of under-represented students, these do not shed light on the complexities underlying the issues of the educationally disadvantaged, such as the…

In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…

This note presents geometric and physical interpretations of the sufficient condition for a critical point to be a strict relative extremum: f[subscript xx]f[subscript yy] - f[superscript 2][subscript xy] greater than 0. The role of the double derivative f[subscript xy] in this inequality will be highlighted in these interpretations. (Contains 14…

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

This article reports a study that investigated the effects of Q-matrix misspecifications on parameter estimates and misclassification rates for the deterministic-input, noisy "and" gate (DINA) model, which is a restricted latent class model for multiple classifications of respondents that can be useful for cognitively motivated diagnostic…

Existing generalizations of the G Index of Agreement of two subjects on n dichotomous items are discussed and an alternative index for ordinal scales with fixed neutral points is proposed. The proposed index can be used as a normalized scalor product and for both item and person similarities. (JKS)

Developed a branch-and-bound algorithm that can be used to seriate a symmetric dissimilarity matrix by identifying a reordering of rows and columns of the matrix optimizing an anti-Robinson criterion. Computational results suggest that with respect to computational efficiency, the approach is generally competitive with dynamic programming. (SLD)

A test for linear trend among a set of eigenvalues of a correlation matrix is described. It is a generalization of G. Anderson's (1965) test for the equality of eigenvalues and extends the present authors' previous work on linear trends in eigenvalues of a covariance matrix. The linear trend hypothesis is discussed. (SLD)

Charles Dodgson (Lewis Carroll) discovered a "curious" method for computing determinants. It is an iterative process that uses determinants of 2 x 2 submatrices of a matrix to obtain a smaller matrix. When the process ends, the result is the determinant of the original matrix. This article discusses both the algorithm and what may have led Dodgson…

Two key concepts arising from Butler's work are the heterosexual matrix--the conflation of sex-gender-sexuality which leads to the normalisation of heterosexuality--and performative reinscription--the discursive process by which the marginalised Other brings new meanings to normative identity constructions. While we have found both concepts…