Elementary Linear Algebra

The book is intended to serve the student as a map through the introductory linear algebra course. To that end it delivers an elementary treatment of linear algebra - suitable for a beginner course for undergraduate students. Our journey shall take us through vectors matrices and their connection to systems of linear equations Gauss-Jordan elimination eigenvalues and diagonalization. Students embarking on a linear algebra course should have a comprehensive knowledge of matrices and vectors. The examples and exercises have been cautiously curated to maintain a symmetry between theory and practice. Over the course of five chapters the book traverses the fundamental material canvassed by most elementary linear algebra courses like vectors matrices system of linear equations eigenvalues and diagonalization. The gears change in Chapter 5 as students reach the introduction of vector spaces and linear transformations. To supplement this core we have also included six appendices devoted to trace and determinant of a matrix minors and cofactors adjoint of a matrix applications of linear equations LU decomposition and finally computer graphics.The aim is to present the student with the essentials of linear algebra in the most lucid and crystalline fashion.Contents:1. Vectors2. Matrices3. System of Linear Equations4. Eigenvalues and Diagonalization5. Vector Spaces and Linear TransformationsAppendix I: Trace and Determinant of a MatrixAppendix II: Minors and CofactorsAppendix III: Adjoint of a MatrixAppendix IV: A pplications of Linear EquationsAppendix V: LU DecompositionAppendix VI: Computer GraphicsSelected BibliographyIndex About the Authors Prof. Dinesh Khattar is currently Principal of Kirori Mal College University of Delhi. He topped and secured the Gold Medal in his B.Sc. As well as M.Sc. Exams at Delhi University. He is a member of the Academic Council Delhi University the highest academic body of the University. He was awarded the Dr. S. Radhakrishnan Memorial National Teacher’s Award in 2015 for his contribution in the field of education. He was also conferred with the prestigious Commonwealth Scholarship for pursuing research in UK. His active involvement in research has allowed him to present papers in eminent international conferences across the globe. Dr. Khattar has been a member of the curriculum development committee for B.Sc. And M.Sc. Programs at various universities including the University of Delhi. He is also an author of more than twenty books on Mathematics including the International Editions: Group Theory and Ring Theory published by Springer Germany and Linear Algebra published by Ane Books. Dr. Neha Agrawal completed her education from Kirori Mal College University of Delhi and pursued her M.Phil. And Ph.D. from University of Delhi. Her areas of research are Nonlinear Dynamical Systems and Chaos Theory. She is working as an Assistant Professor at the Department of Mathematics Kirori Mal College since 2012 and has also taught in other prestigious colleges like Miranda House Daulat Ram and NSIT. She has published several research papers in reputed international journals. She is also the co-author of the books Group Theory Ring Theory and Linear Algebra. Dr. Prempal Singh is an Assistant Professor at the Department of Mathematics Kirori Mal College University of Delhi. He completed his Ph.D from University of Delhi in the year 2010. He has published research papers in reputed National and international journals. His areas of research include Operator Theory Non-linear Dynamical Systems and Chaos Synchronization Differential Equations and Mathematical Modelling Vedic Mathematics and Astronomy Traffic Flow Problems Air Pollution Problems Risk Assessment Analysis and Floods History of Indian Monuments and Scientific Architecture Mathematical Modelling of Covid- 19 etc. He has more than 18 years of experience in undergraduate and postgraduate teaching in the Department of Mathematics as well in various colleges of University of Delhi.

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