Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup
This thesis is submitted in a partial fulfilment of the requirements for the degree of Bachelor of Science in Mathematics 2018.
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BRAC University
2018
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| Acceso en línea: | http://hdl.handle.net/10361/10824 |
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10361-10824 |
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10361-108242019-09-30T05:55:51Z Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup Shiham, Muhtadi Nasrullah Ahmed, Mohammad Maruf Department of Mathematics and Natural Sciences, BRAC University Linear equations Differential equations, Linear. This thesis is submitted in a partial fulfilment of the requirements for the degree of Bachelor of Science in Mathematics 2018. Catalogued from PDF version of thesis. Includes bibliographical references (page 33). There are a number of versatile generalizations of the usual inverse matrix, referred to in this thesis as generalized inverse matrices. The definitions and properties of some of the common generalized inverse matrices are described, including methods for constructing them. A number of applications are discussed, including their use in solving consistent systems of linear equations which do not have the same number of equations as variables, or which have a singular coefficient determinant. A certain type of generalized inverse is shown to give the least‐squares solution of an inconsistent system of linear equations. Other applications are to systems of nonlinear equations, to integer solutions of systems of equations and to linear programming. The purpose of the thesis is to show that a singular or 𝑚×𝑛 matrix has a generalized inverse (g-inverse). A matrix 𝐴− is said to be a generalized inverse if it fulfils the condition 𝐴𝐴−𝐴=𝐴. The raw canonical system is used to find the generalized inverse. So we will be using theorems, examples and programming language to prove and solve G-inverse. This thesis will also consist of semigroups, contour integration and applications which is related generalized inverse. Muhtadi Nasrullah Shiham B. Mathematics 2018-11-08T03:45:24Z 2018-11-08T03:45:24Z 2018 2018-09-27 Thesis ID 12216002 http://hdl.handle.net/10361/10824 en BRAC University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 33 pages application/pdf BRAC University |
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Brac University |
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Institutional Repository |
| language |
English |
| topic |
Linear equations Differential equations, Linear. |
| spellingShingle |
Linear equations Differential equations, Linear. Shiham, Muhtadi Nasrullah Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| description |
This thesis is submitted in a partial fulfilment of the requirements for the degree of Bachelor of Science in Mathematics 2018. |
| author2 |
Ahmed, Mohammad Maruf |
| author_facet |
Ahmed, Mohammad Maruf Shiham, Muhtadi Nasrullah |
| format |
Thesis |
| author |
Shiham, Muhtadi Nasrullah |
| author_sort |
Shiham, Muhtadi Nasrullah |
| title |
Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| title_short |
Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| title_full |
Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| title_fullStr |
Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| title_full_unstemmed |
Generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| title_sort |
generalized inverse and it’s applications to the solutions of system of linear equations and semigroup |
| publisher |
BRAC University |
| publishDate |
2018 |
| url |
http://hdl.handle.net/10361/10824 |
| work_keys_str_mv |
AT shihammuhtadinasrullah generalizedinverseanditsapplicationstothesolutionsofsystemoflinearequationsandsemigroup |
| _version_ |
1814306826440671232 |