The objectives of the course are to introduce students to the basic ideas and methods of linear algebra and enable them to understand the idea of a ring, field , groups matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices and be aware of examples of these structures in mathematics and physics.

Learning Outcomes

At the end of the course the students will be able to:

Use computational techniques and algebraic skills essential for the study of systems of linear equations, matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and diagonalization. (Computational and Algebraic Skills).
Use technology, where appropriate, to enhance and facilitate mathematical understanding, as well as an aid in solving problems and presenting solutions(Technological Skills).
Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra. (Proof and Reasoning).

Course outline:

Matrices: Addition, Multiplication, Transpose, Matrices and Systems of Linear Equations, Block Matrices. Polynomial in Matrices, Invertible Matrices, Complex Matrices, Elementary Matrices and Applications, Quadratic Forms, Simlarity.
Vector Space: Vector Spaces, Subspaces, Linear Combination, Linear Spans, Basis and Dimension, Linear Combination and Vector Space, Change of Basis. Orthogonality, Inner Product Spaces.
Cauchy-Schwarz Inequality, Applications.
Porjections, Inner Products and Matrices, Normed Vector Spaces.

Recommended Books:

1. Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill
2. Mathematical Methods for Physicists by George Arfken and Hans J. Weber, (6th and onwards editions)
Acad Press.