This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering. It has a more significant application in information sciences and control theory.
A definition of linear algebra is that it is a part of algebra which is concerned with equations of the first degree. Thus, at the fundamental level, it involves the discussion of matrices and determinants, and the solutions of systems of linear equations, which have a wide application in further discussion of this subject.
Technical topics discussed in the book include:
- Matrices
- Vector spaces
- Eigenvalue and eigenvectors
- Linear transformation
- Inner product spaces
- Diagonalizations
- Applications to conics and quadrics
- Canonical forms
- Least squares problems.
This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering.
1. Matrices
2. System of Linear Equations and Determinants
3. Vector Spaces
4. Eigenvalues and Eigenvectors
5. Linear Transformation
6. Inner Product Spaces
7. Matrix Representation of Linear Transformations
8. Diagonalizations
9. Application to Conics and Quadrics
10. Canonical Forms
11. Least Square Problems
Ramakanta Meher currently works as an Associate Professor at Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat, India. His current research interests include differential and integral equations, fractional differential equations, linear algebra, approximation theory, numerical analysis, and fuzzy set theory. He has supervised 7 Ph.D. students and 30 M.Sc. students, and oversees 6 additional Ph.D. students. He has published over 80 international research publications in various SCI-indexed Q1 and Q2 international journals and solely published 7 textbooks. He has coordinated many prestigious programmes such as Mathematics Training Talent Search Programme (MTTS)-2013 (Level-0,1 and 2) sponsored by National Board of Higher Mathematics (NBHM), two STTPs by receiving grants from the Indian Society of Technical Education, New Delhi and some STTPs by receiving grants from TEQIP and SVNIT, Surat. He has delivered a series of invited talks at several scientific events held in India, Thailand, Saudi Arabia, Dubai, Mongolia, and South Africa. He has received several international travel grants such as the CIMPA-KAUST Travel Grant to visit King Abdullah University of Science and Technology, Thuwal, Saudi Arabia in 2012, CIMPA-UNESCO-MESR-MICINN-APSA-SOUTH AFRICA Travel Grant to visit African Institute of Mathematical Sciences, Muizenberg, Cape town, South Africa in 2011, CIMPA-UNESCO-MICINN-THAILAND Travel Grant to visit Chulalongkorn University, Bangkok, Thailand in 2011 and CIMPA-UNESCO-SCHOOL MONGOLIA Travel Grant to visit Mongolian State University, Mongolia in 2013.
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