Provides a comprehensive textbook of linear algebra
Includes a number of solved examples, exercises and applications
Presents applications of linear algebra in analytical geometry and numerical methods
MOHAMMAD ASHRAF is Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 1986, with the thesis titled "A study of certain commutativity conditions for associative rings”. He has authored over 200 research publications in various areas of mathematics such as ring theory, coding theory and graph theory. He is a recipient of the Young Scientist's Award (1988) from Indian Science Congress Association, I.M.S. Prize (1995) from Indian Mathematical Society, and the Ziauddin Gold Medal for securing first position at M.Sc. examination in the year 1981. He is presently dealing with two major research projects awarded by the Department of Science and Technology in the area of derivations in rings. His research interests include ring theory/commutativity and structure of rings and near-rings, derivations on rings, near-rings and Banach algebras, functional identities in rings and algebras, applied linear algebra, algebraic coding theory, cryptography, and graph theory.
VINCENZO DE FILIPPIS is Associate Professor at the Department of Mathematics, University of Messina, Italy. He completed his Ph.D. in Mathematics from the University of Messina, Italy, in 1999 with the thesis titled "Leads in rings first”. His research articles have been published in journals and conference proceedings of repute. He is the recipient of the Young Researcher Prize by the University of Messina, Italy, in 2005.
MOHAMMAD ASLAM SIDDEEQUE is Assistant Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 2014 with the thesis titled "On derivations and related mappings in rings and near-rings". His area of research includes the study of derivations over rings and near-rings on which he has published research articles in journals of repute.
This book is a comprehensive textbook of linear algebra and intends at presenting new approaches for existing concepts and applications. The book starts with a quick review of basic literature on groups, rings and fields—the essential components for defining a vector space over a field—and ends with the applications of linear algebra in analytical geometry and numerical methods in its last two chapters. It also includes a number of exercises and examples at the end of each chapter to enhance the understanding of readers. The subject is developed in a manner accessible to students with little knowledge of linear algebra.
1. Algebraic Structures.- 2. Matrices and Systems of Linear Equations.- 3. Vector Spaces.- 4. Linear Transformations.- 5. Dual Spaces.- 6. Inner Product Spaces.- 7. Canonical Forms of an Operator.- 8. Bilinear and Quadratic Forms.- 9. Sesquilinear and Hermitian Forms.- 10. Affine and Euclidean Spaces and the Applications of Linear Algebra to Geometry.
As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical forms of an operator and bilinear and quadratic forms.
This book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical, bilinear, quadratic, sesquilinear, Hermitian forms of operators and tensor products of vector spaces with their algebras. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each section to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings, etc., has been pre-assumed.
Algebraic Structures.- Matrices and Systems of Linear Equations.- Vector Spaces.- Linear Transformations.- Dual Spaces.- Inner Product Spaces.- Canonical Forms of an Operator.- Bilinear and Quadratic Forms.- Sesquilinear and Hermitian Forms.- Applications of Linear Algebra to Numerical Methods.- Affine and Euclidean Spaces and the Applications of Linear Algebra to Geometry.- Ordinary differential equations and linear systems of ordinary differential equations.
Mohammad Ashraf is Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in the year 1986. After completing his Ph.D., he started his teaching career as Lecturer at the Department of Mathematics, Aligarh Muslim University, elevated to the post of Reader in 1987 and then became Professor in 2005. He also served as Associate Professor at the Department of Mathematics, King Abdulaziz University, KSA, from 1998 to 2004.
His research interests include ring theory/commutativity and structure of rings and near-rings, derivations on rings, near-rings & Banach algebras, differential identities in rings and algebras, applied linear algebra, algebraic coding theory and cryptography. With a teaching experience of around 35 years, Prof. Ashraf has supervised the Ph.D. thesis of 13 students and is currently guiding 6 more. He has published around 225 research articles in internationaljournals and conference proceedings of repute. He received the Young Scientist's Award from Indian Science Congress Association in the year 1988 and the I.M.S. Prize from Indian Mathematical Society for the year 1995. He has completed many major research projects from the UGC, DST and NBHM. He is also Editor/ Managing Editor of many reputed international mathematical journals.
Vincenzo De Filippis is Associate Professor of Algebra at the University of Messina, Italy. He completed his Ph.D. in Mathematics from the University of Messina, Italy, in 1999. He is the member of the Italian Mathematical Society (UMI) and National Society of Algebraic and Geometric Structures and their Applications (GNSAGA). He has published around 100 research articles in reputed journals and conference proceedings.
Mohammad Aslam Siddeeque is Associate Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 2014 with the thesis entitled "On derivations and related mappings in rings and near-rings". His research interest lies in derivations and its various generalizations on rings and near-rings, on which he has published articles in reputed journals.
Über den Autor
Mohammad Ashraf is Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in the year 1986. After completing his Ph.D., he started his teaching career as Lecturer at the Department of Mathematics, Aligarh Muslim University, elevated to the post of Reader in 1987 and then became Professor in 2005. He also served as Associate Professor at the Department of Mathematics, King Abdulaziz University, KSA, from 1998 to 2004.
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His research interests include ring theory/commutativity and structure of rings and near-rings, derivations on rings, near-rings & Banach algebras, differential identities in rings and algebras, applied linear algebra, algebraic coding theory and cryptography. With a teaching experience of around 35 years, Prof. Ashraf has supervised the Ph.D. thesis of 13 students and is currently guiding 6 more. He has published around 225 research articles in international journals and conference proceedings of repute. He received the Young Scientist's Award from Indian Science Congress Association in the year 1988 and the I.M.S. Prize from Indian Mathematical Society for the year 1995. He has completed many major research projects from the UGC, DST and NBHM. He is also Editor/ Managing Editor of many reputed international mathematical journals.
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Vincenzo De Filippis is Associate Professor of Algebra at the University of Messina, Italy. He completed his Ph.D. in Mathematics from the University of Messina, Italy, in 1999. He is the member of the Italian Mathematical Society (UMI) and National Society of Algebraic and Geometric Structures and their Applications (GNSAGA). He has published around 100 research articles in reputed journals and conference proceedings.
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Mohammad Aslam Siddeeque is Associate Professor at the Department of Mathematics, Aligarh Muslim University, India. He completed his Ph.D. in Mathematics from Aligarh Muslim University, India, in 2014 with the thesis entitled "On derivations and related mappings in rings and near-rings". His research interest lies in derivations and its various generalizations on rings and near-rings, on which he has published articles in reputed journals.
Inhaltsverzeichnis
1. Algebraic Structures
2. Matrices and Systems of Linear Equations
3. Vector Spaces
4. Linear Transformations
5. Dual Spaces
6. Inner Product Spaces
7. Canonical Forms of an Operator
8. Bilinear and Quadratic Forms
9. Sesquilinear and Hermitian Forms
10. Applications of Linear Algebra to Numerical Methods
11. Affine and Euclidean Spaces and the Applications of Linear Algebra to Geometry
12. Ordinary differential equations and linear systems of ordinary differential equations
Klappentext
This book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical, bilinear, quadratic, sesquilinear, Hermitian forms of operators and tensor products of vector spaces with their algebras. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each section to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings, etc., has been pre-assumed.
Gives complete and comprehensive coverage of major topics in algebra
Contains a rich collection of solved examples and exercises for practice
Discusses applications in numerical methods, analytical geometry, and solving linear system of DE
