In this note the well-known Lagrange identity is extended to matrices. The resulting generalized Lagrange identity is used to give characterizations of symmetry, commutativity of projectors and normality.

In this note 4 x 4 most-perfect pandiagonal magic squares are considered in which rows, columns and the two main, along with the broken, diagonals add up to the same sum. It is shown that the Moore-Penrose inverse of these squares has the same magic property.

The well-known Frobenius rank inequality established by Frobenius in 1911 states that the rank of the product ABC of three matrices satisfies the inequality rank(ABC) [greater than or equal]rank(AB) + rank(BC) - rank(B) A new necessary and sufficient condition for equality to hold is presented and then some interesting consequences and…

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…

The information matrix for the parameters in a latent-variable model is bounded from above by the information that would obtain if the values of the latent variables could also be observed. The difference is the "missing information." This paper discusses the structure of the information matrix, and characterizes the degree to which…

The one observation per cell two-way items by examinees random effects analysis of variance (ANOVA) with all error components zero is considered. The estimated variance components are expressed as functions of the inter-item covariance matrix and the inter-examinee covariance matrix. These expressions show that under the random effects model if…

The one observation per cell two-way items by examinees random effects analysis of variance (ANOVA) with all error components zero is considered. The estimated variance components are expressed as functions of the inter-item covariance matrix and the inter-examinee covariance matrix. These expressions show that under the random effects model if…

A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…

Peay presented a class of grouping methods based on the concept of the r-clique for symmetric data relationships. The concepts of the r-clique can be generalized readily to directed (or asymmetric) relationships, and groupings based on this generalization may be found conveniently using an adoption of Peay's methodology. (Author/BJG)

Canonical analysis is frequently used in studies of relationships between sets of variables which are difficult to measure accurately, partly because of the true nature of the data and partly because of errors associated with the measurement instruments. Meredith's solution to the fallible data problem is examined. (Author/BJG)

This paper presents a revised and updated version of a FORTRAN program which computes all indices used in the Flanders' Interaction Matrix. The new program has added another form of data input which simplifies data entry. The new version also has the capability of interactive terminal use. (Author)

Three dissimilarity measures for the unconstrained sorting task are investigated. All three are metrics, but differ in the kind of compensation which they make for differences in the sizes of cells within sortings. Empirical tests of the measures are done with sorting data for occupations names and the names of behaviors, using multidimensional…

A generalized matrix procedure is developed for computing the proportionate contribution of a factor, either orthogonal or oblique, to the total common variance of a factor solution. (Author)