Diagnostic classification models (DCMs) are structured latent class models widely discussed in the field of psychometrics. They model subjects' underlying attribute patterns and classify subjects into unobservable groups based on their mastery of attributes required to answer the items correctly. The effective implementation of DCMs depends…

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.

The problem of estimating the cross-product of two mean vectors in three-dimensional Euclidian space is considered. Two "natural" estimators are developed, both of which turn out to be biased. A third, unbiased estimator, resulting from a jackknife procedure, is also investigated. It is shown that, under normality, the latter is best among all the…

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

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…

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…