User talk:Chikjib

Jibunoh's Method For Evaluating the Determinant of an N x N matrix
Chafa C. Jibunoh Email: chafa_chid@yahoo.com GSM: +2348053336496 Department of Mathematics and Statistics Delta State Polytechnic Ogwashi-Uku Nigeria

As delivered to the Nigerian Mathematical Society (NMS) in the conference of June 2009, at Ilorin, Nigeria. Abstract A simple and systematic procedure for obtaining the determinant of any n x n matrix without the use of cofactors is developed in this paper. The procedure involves reduction of the square matrix to echelon form and dividing the product of the diagonal elements by the product of some numbers defined as lower multipliers. The simplicity of the procedure is maintained and appreciated as the order of the matrix, n →∞. This makes it superior to the traditional method of cofactors which is often tedious to apply in high order matrices.

PREFACE It has been a normal practice to publish a research discovery in an appropriate Journal meant for specialists in the field of the research or other persons who may be interested in the results. In many cases, not every specialist gets in touch with the Journal, especially if it is not in regular circulation. Where a research result is not mainly of specialists’ interest but addresses a problem that cuts across many disciplines, I am of the opinion that the discovery could also be published as a monograph which can be circulated promptly by a publisher. The paper ‘The Determinant of an n x n matrix by reduction to echelon form’ is a baby of many disciplines and has been in high demand since it was presented to the Nigerian Mathematical Society (NMS), in the Annual Conference of June 2009, at Ilorin, Nigeria. Rather than responding to the requests for photocopies of the paper, I considered it appropriate to place the exact paper in a publication as a monograph. As pointed out, the idea of a determinant of a matrix is not mainly for mathematicians or statisticians per se. It is useful to engineers, technologists, scientists, social scientists, computer scientists, business administrators, accountants or other persons involved in matrices, quantitative techniques or empirical evaluations. The knowledge of determinant is required at all levels of study, from school certificate level to post graduate studies and beyond. The spectacular aspect of the monograph is that it presents a new, simpler and systematic method of evaluating the determinant of an n x n matrix, no matter how large the value of n. The traditional method which uses minor determinants or cofactors is often tedious when n is large and is now outdated. This new and simple method which is a product of research may be referred to as Jibunoh’s method for evaluating the determinant of an n x n matrix. I wish to thank many senior colleagues of the Nigerian Mathematical Society for encouraging me to reproduce this paper for wider dissemination. Conclusion to the Work The procedure of obtaining the determinant of an n x n matrix by reduction to echelon form as described in this paper is systematic and simple. It has obvious advantage over the traditional method of cofactors which is tedious to apply as n →∞. The beauty of this procedure is easily appreciated in those cases where the square matrices are of high orders greater than three.

Dr. C.C. Jibunoh Ogwashi-Uku, Nigeria 15th July, 2009

This monograph is for Sale.

Interested persons may contact the author using the following contact information;

Dr.C.C. Jibunoh Department of Mathematics and Statistics Delta State Polytechnic, Ogwashi-Uku, Nigeria Email: chafa_chid@yahoo.com GSM: +2348053336496

Jibunoh's Method For Evaluating the Determinant of an N x N matrix
Chafa C. Jibunoh Email: chafa_chid@yahoo.com GSM: +2348053336496 Department of Mathematics and Statistics Delta State Polytechnic Ogwashi-Uku Nigeria

As delivered to the Nigerian Mathematical Society (NMS) in the conference of June 2009, at Ilorin, Nigeria. Abstract A simple and systematic procedure for obtaining the determinant of any n x n matrix without the use of cofactors is developed in this paper. The procedure involves reduction of the square matrix to echelon form and dividing the product of the diagonal elements by the product of some numbers defined as lower multipliers. The simplicity of the procedure is maintained and appreciated as the order of the matrix, n →∞. This makes it superior to the traditional method of cofactors which is often tedious to apply in high order matrices.

PREFACE It has been a normal practice to publish a research discovery in an appropriate Journal meant for specialists in the field of the research or other persons who may be interested in the results. In many cases, not every specialist gets in touch with the Journal, especially if it is not in regular circulation. Where a research result is not mainly of specialists’ interest but addresses a problem that cuts across many disciplines, I am of the opinion that the discovery could also be published as a monograph which can be circulated promptly by a publisher. The paper ‘The Determinant of an n x n matrix by reduction to echelon form’ is a baby of many disciplines and has been in high demand since it was presented to the Nigerian Mathematical Society (NMS), in the Annual Conference of June 2009, at Ilorin, Nigeria. Rather than responding to the requests for photocopies of the paper, I considered it appropriate to place the exact paper in a publication as a monograph. As pointed out, the idea of a determinant of a matrix is not mainly for mathematicians or statisticians per se. It is useful to engineers, technologists, scientists, social scientists, computer scientists, business administrators, accountants or other persons involved in matrices, quantitative techniques or empirical evaluations. The knowledge of determinant is required at all levels of study, from school certificate level to post graduate studies and beyond. The spectacular aspect of the monograph is that it presents a new, simpler and systematic method of evaluating the determinant of an n x n matrix, no matter how large the value of n. The traditional method which uses minor determinants or cofactors is often tedious when n is large and is now outdated. This new and simple method which is a product of research may be referred to as Jibunoh’s method for evaluating the determinant of an n x n matrix. I wish to thank many senior colleagues of the Nigerian Mathematical Society for encouraging me to reproduce this paper for wider dissemination. Conclusion to the Work The procedure of obtaining the determinant of an n x n matrix by reduction to echelon form as described in this paper is systematic and simple. It has obvious advantage over the traditional method of cofactors which is tedious to apply as n →∞. The beauty of this procedure is easily appreciated in those cases where the square matrices are of high orders greater than three.

Dr. C.C. Jibunoh Ogwashi-Uku, Nigeria 15th July, 2009

This monograph is for Sale.

Interested persons may contact the author using the following contact information;

Dr.C.C. Jibunoh Department of Mathematics and Statistics Delta State Polytechnic, Ogwashi-Uku, Nigeria Email: chafa_chid@yahoo.com GSM: +2348053336496

--Chikjib (talk) 19:45, 23 October 2012 (UTC)

MATRIX INVERSIONS VIA JIBUNOH'S DETERMINANTS & EXACT SOLUTIONS OF K X K SYSTEMS OF LINEAR EQUATIONS
MATRIX INVERSIONS VIA JIBUNOH'S DETERMINANTS AND

EXACT SOLUTIONS OF K X K SYSTEMS OF LINEAR

EQUATIONS

BY

CHAFA C. JIBUNOH

(chafa_chid@yahoo.com, +2348053336496)

Department of Mathematics and Statistics

Delta State Polytechnic, Ogwashi - Uku, Nigeria

As presented in a workshop at the National Mathematical Centre, Abuja, Nigeria

June, 2010

Abstract:A simple and systematic procedure for solving any k x k system of linear equations is developed in this paper. The determinant of the equation matrix is first found using Jibunoh's method. Then the matrix is inverted by applying the defined backward vector substitutions (bvs). The reciprocal of the positive value of the determinant, if the matrix is real, is taken as a factor of the inverse matrix. The complex matrix is similarly inverted to obtain what is defined as either the Analytical or Empirical inverse. The entries of any inverse matrix (real or complex) are mainly integers, without the scalar-factor multiplying the matrix. This makes the inverse matrix exact and more accurate than decimal representations obtained by computer evaluations. For any system of equations, therefore, three quantities are obtained simultaneously, namely, the determinant of the equation matrix, the inverse of the matrix and the solution of the system. The production of these quantities simultaneously, is new in the literature. By these procedures, any linear system of equations of dimensions k can be solved easily and accurately, as k →∞.

PREFACE

My previous work on Determinants, namely 'Jibunoh's method for evaluating the determinant of an n x n matrix; a monograph on research discovery' focused on a new and simple approach for evaluating the determinant of any n x n matrix, by reduction to echelon form. This approach demonstrated superiority(in terms of more simplicity) over the traditional method of cofactors which is tedious to apply when n is large. The contents of 'Jibunoh's determinants' gained popularity after the initial presentation to the Nigerian Mathematical Society (NMS) in the conference of June 2009, at Ilorin, Nigeria.

In 2010, it became necessary to extend the concept of Jibunoh's determinants to the quick and exact evaluation of inverses of k x k matrices, no matter how large the value of k. This naturally resulted in obtaining the exact numerical solutions of any corresponding     k x k systems of linear equations. The work was also a product of research which was first presented in a workshop at the National Mathematical Centre, Abuja, in June 2010, where it was received with great enthusiasm. The Abuja presentation formed the contents of the current monograph which now bears the title 'Matrix inversions via Jibunoh's determinants and exact solutions of k x k systems of linear equations'

I expect that the monograph should be a companion to my first monograph of 2009 which has circulated widely and which should be studied in order to grasp the simple but technical aspect of matrix inversions via Jibunoh's determinants. Nevertheless, the current monograph has been made to be relatively simple and self contained.

As usual, I recommend the monograph not only to mathematicians or statisticians per se, but to engineers, technologists, social scientists, business administrators, accountants, computer scientists etc, including students in these fields who are in the secondary and tertiary institutions. They will appreciate the simplicity of the new method of matrix inversions and the beauty of obtaining the exact solutions of k x k systems of linear systems.

I must thank the National Mathematical Centre, Abuja, for creating a workshop in 2010, during which I gave my maiden presentation. I should not fail to thank my colleagues in the Nigerian Mathematical Society and my children, friends and relatives for their moral support and encouragement.

Dr C. C. Jibunoh

Ogwashi - Uku, Nigeria

25th November, 2010

Conclusion to the Work

The procedure of obtaining the inverse of any square matrix or solving a k x k system of linear equations via Jibunoh's determinants, is obviously easier than the traditional application of cofactors, Gaussian elimination, or iterative methods in the literature. The procedure gives the exact inverse of a real or complex matrix and exact solutions of systems. In the inversion of a complex matrix, we obtain what is defined as either the Analytical or Empirical inverse. The entries of all inverse matrices are mainly integers (without the multiplying factors). Hence the procedure is superior, in accuracy to computer solutions which are usually decimal representations.

Even though the present application of Jibunoh's method is manual, it can evaluate with computational ease any k x k matrix or system, as k →∞. We may, however, note that in finding determinants, a computer program of Jibunoh' method is possible. But for matrix inversions, the snag is whether, as in Jibunoh's method, the computer program can retain the entries of the inverse matrices as integers or rational numbers, without decimals. This aspect needs investigation, especially in this age of automation.

Dr C. C. Jibunoh

Ogwashi - Uku, Nigeria

25th November, 2010

This monograph is for Sale.

Interested persons may contact the author using the following contact information;

Email: Chafa_chid@yahoo.com

Phone: +2348053336496

--Chikjib (talk) 19:52, 23 October 2012 (UTC)

Speedy deletion nomination of Sam Agbamuche


A tag has been placed on Sam Agbamuche, requesting that it be deleted from Wikipedia. This has been done under two or more of the criteria for speedy deletion, by which pages can be deleted at any time, without discussion. If the page meets any of these strictly-defined criteria, then it may be soon be deleted by an administrator. The reasons it has been tagged are:
 * It seems to be unambiguous advertising which only promotes a company, product, group, service or person and would need to be fundamentally rewritten in order to become encyclopedic. (See section G11 of the criteria for speedy deletion.) Please read the guidelines on spam and FAQ/Business for more information.
 * It appears to be about a person, organization (band, club, company, etc.), individual animal, or web content, but it does not indicate how or why the subject is important or significant: that is, why an article about that subject should be included in an encyclopedia. (See section A7 of the criteria for speedy deletion.) Such articles may be deleted at any time. Please see the guidelines for what is generally accepted as notable.

If you think this page should not be deleted for this reason, you may contest the nomination by visiting the page and clicking the button labelled "Contest this speedy deletion". This will give you the opportunity to explain why you believe the page should not be deleted. However, be aware that once a page is tagged for speedy deletion, it may be removed without delay. Please do not remove the speedy deletion tag from the page yourself, but do not hesitate to add information in line with Wikipedia's policies and guidelines. If the page is deleted, and you wish to retrieve the deleted material for future reference or improvement, then please contact the deleting administrator, or if you have already done so, you can place a request here. Valenciano (talk) 21:37, 13 December 2016 (UTC)