Advanced Linear Algebra with Applications

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

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 with the thesis entitled "A study of certain commutativity conditions for associative rings". 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 30 years, Prof. Ashraf has supervised the Ph.D. thesis of 7 students and is currently guiding 6 more. He has published around 161 research articles in 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.

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 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 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.