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…

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…

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Examples for determining the equation of a line through two points or a quadratic function that contains three noncollinear points are presented. (MNS)

Provides an activity as an example of how matrices can be introduced from finite graphs and how finite graphs can be analyzed by examining their matrix representations. Presents the materials, objectives, prerequisites, directions, extension activities, answers, and worksheets. (YP)

Provides an overview of a course, "Applied Linear Algebra," for teaching the concepts and the physical and geometric interpretations of some linear algebra topics. Describes the philosophy of the course, the computer project assignments, and student feedback. Major topics of the course are listed. (YP)

Described are procedures for multiplying matrices using Logo. Examples of computer programming are included. (RH)

Provides a program listing in True BASIC which constructs several kinds of matrices: (1) matrices with integral entries that have inverses that have integral entries; (2) matrices with integral entries that have inverses that are rational numbers with reasonable denominators; and (3) matrices with integral entries and prescribed integer…