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Rani, Narbda; Mishra, Vinod – International Journal of Mathematical Education in Science and Technology, 2022
This paper contains interesting facts regarding the powers of odd ordered special circulant magic squares along with their magic constants. It is shown that we always obtain circulant semi-magic square and special circulant magic square in the case of even and odd positive integer powers of these magic squares respectively. These magic squares…
Descriptors: Numbers, Mathematical Logic, Mathematics Education, Mathematical Concepts
Debnath, L. – International Journal of Mathematical Education in Science and Technology, 2014
This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…
Descriptors: Matrices, Mathematics Instruction, Mathematical Concepts, Geometry
Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2013
An elementary proof using matrix theory is given for the following criterion: if "F"/"K" and "L"/"K" are field extensions, with "F" and "L" both contained in a common extension field, then "F" and "L" are linearly disjoint over "K" if (and only if) some…
Descriptors: Mathematical Logic, Validity, Algebra, Matrices
Aversa, Vincenzo; De Simone, Anna – International Journal of Mathematical Education in Science and Technology, 2012
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.
Descriptors: Geometric Concepts, College Mathematics, Undergraduate Study, Mathematics Instruction
Usaini, S. – International Journal of Mathematical Education in Science and Technology, 2012
An involutory matrix is a matrix that is its own inverse. Such matrices are of great importance in matrix theory and algebraic cryptography. In this note, we extend this involution to rhotrices and present their properties. We have also provided a method of constructing involutory rhotrices.
Descriptors: Mathematics Instruction, Matrices, Equations (Mathematics), Validity
Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2012
This note explains how Emil Artin's proof that row rank equals column rank for a matrix with entries in a field leads naturally to the formula for the nullity of a matrix and also to an algorithm for solving any system of linear equations in any number of variables. This material could be used in any course on matrix theory or linear algebra.
Descriptors: Matrices, Mathematics Instruction, Validity, Mathematical Logic
Chang, J.-M. – International Journal of Mathematical Education in Science and Technology, 2011
Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…
Descriptors: Inquiry, Mathematics Instruction, College Mathematics, Teaching Methods
Stewart, Sepideh; Thomas, Michael O. J. – International Journal of Mathematical Education in Science and Technology, 2010
One of the earlier, more challenging concepts in linear algebra at university is that of basis. Students are often taught procedurally how to find a basis for a subspace using matrix manipulation, but may struggle with understanding the construct of basis, making further progress harder. We believe one reason for this is because students have…
Descriptors: Mathematics Instruction, Algebra, Mathematical Concepts, College Mathematics
Keskin, Refik; Demirturk, Bahar – International Journal of Mathematical Education in Science and Technology, 2010
The aim of this article is to characterize the 2 x 2 matrices "X" satisfying X[superscript 2] = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers. The recommendations regarding the teaching of the identities given in this article can be presented in two cases. The first is related to the pedagogical aspect. The…
Descriptors: Mathematics Instruction, Numbers, Algebra, Student Motivation
Kanwar, V.; Sharma, Kapil K.; Behl, Ramandeep – International Journal of Mathematical Education in Science and Technology, 2010
In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…
Descriptors: Geometric Concepts, Equations (Mathematics), Matrices, Mathematics Instruction
Khalili, Parviz – International Journal of Mathematical Education in Science and Technology, 2009
We will prove a well-known theorem in Linear Algebra, that is, for any "m x n" matrix the dimension of row space and column space are the same. The proof is based on the subject of "elementary matrices" and "reduced row-echelon" form of a matrix.
Descriptors: Matrices, Equations (Mathematics), Transformations (Mathematics), Mathematical Logic
Radhakrishnan, R.; Choudhury, Askar – International Journal of Mathematical Education in Science and Technology, 2009
Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…
Descriptors: Computers, Multivariate Analysis, Matrices, Mathematics Instruction
Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2009
The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical induction or the well-ordering principle. The method of iteration depends only on the fact that any strictly decreasing sequence of…
Descriptors: Logical Thinking, Mathematical Logic, Calculus, Matrices
Sani, B. – International Journal of Mathematical Education in Science and Technology, 2008
In this note, a method of converting a rhotrix to a special form of matrix termed a "coupled matrix" is proposed. The special matrix can be used to solve various problems involving n x n and (n - 1) x (n - 1) matrices simultaneously.
Descriptors: Mathematics Instruction, Matrices, Problem Solving, Equations (Mathematics)
Trenkler, G.; Trenkler, D. – International Journal of Mathematical Education in Science and Technology, 2008
Using the elementary tools of matrix theory, we show that the product of two rotations in the three-dimensional Euclidean space is a rotation again. For this purpose, three types of rotation matrices are identified which are of simple structure. One of them is the identity matrix, and each of the other two types can be uniquely characterized by…
Descriptors: Matrices, Geometric Concepts, Mathematics Instruction, Geometry
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