Define the centre of a parallelogram to be the intersection of its diagonals. It was shown in an earlier paper that the intersection of arbitrarily many parallelograms with the same centre is the unit disc about that centre in a metric defined using ideas from Linear Algebra. In this note, it is shown that this characterizes compact, convex sets,…

This paper reports on the effects the use of a pocket calculator-based computer algebra system (CAS) has on the performance in mathematics of grade 11 students in Germany. A project started at 8 of about one hundred upper secondary schools in the federal state of Thuringia in 1999; 3 years later the former restrictions on the use of technology in…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

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

In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

In this note, an integrated form of some significant means with two variables is provided, and some chains for mean value inequalities are obtained. At the same time, a concise family of algebraic functions appears, which satisfy Mitrinovic's requirements.

A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…

In this article, an alternative multiplication method for rhotrices is proposed. The method establishes some relationships between rhotrices and matrices. This article has discussed a modified multiplication method for rhotrices. The method has a direct relationship with matrix multiplication, and so rhotrices under this multiplication procedure…

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.