Characteristic polynomials are used to determine when magic squares have magic inverses. A resulting method constructs arbitrary examples of such squares.

Two methods for solving matrix equations are discussed. Both operate entirely on a matrix level. (MNS)

The matrix diagonalization method is used to solve a limit problem.

In this note it is shown that the Moore-Penrose inverse of real 3 x 3 matrices can be expressed in terms of the vector product of their columns. Moreover, a simple formula of a generalized inverse is presented, which also involves the vector product.

This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…

An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

Two statements concerning magic squares, considered as 3x3 matrices, are discussed and their proofs given using only high school level techniques. (MP)

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

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…