Course

Vector Spaces: Vector spaces – Sub spaces – Linear independence – Basis – Dimension.
(10 hrs)

Inner Product Spaces: Inner products – Orthogonality – Orthogonal basis – Gram Schmidt Process – Change of basis – Orthogonal complements – Projection on subspace – Least Square Principle. QR- Decomposition. (10 hrs)

Linear Transformations: Linear transformation – Relation between matrices and linear transformations – Kernel and range of a linear transformation – Change of basis. Symmetric and Skew Symmetric Matrices, Adjoint and Hermitian Adjoint of a Matrix. (10 hrs)

Eigen values and Eigen vectors: Eigen Values and Eigen Vectors, Diagonalization, Orthogonal Diagonalization, Quadratic Forms, Diagonalizing Quadratic Forms, Conic Sections. Similarity of linear transformations – Diagonalisation and its applications. 

Solving system of equations using Guess iterative methods. Power method for eigenvalue and eigenvector. (12 hrs)

Course Objectives:

Understand the basic concepts of vector space, subspace, basis and dimension.

Familiar the inner product space. Finding the orthogonal vectors using inner product.

Understand and apply linear transform for various matrix decompositions.

Course Outcomes:

CO1: To Understand the basic concepts of vector space, subspace, basis and dimension.

CO2: To Understand the basic concepts of inner product space, norm, angle, Orthogonality and projection and implementing the Gram-Schmidt process, to obtain least square solution

CO3: To Understand the concept of linear transformations, the relation between matrices and linear transformations, kernel, range and apply it to change the basis and to transform the given matrix to diagonal form.

CO4: To understand the eigen values and eigen vectors and apply to transformation problems.

Text Book:

Howard Anton and Chris Rorres, “Elementary Linear Algebra”, Tenth Edition, John Wiley & Sons, 2010.

References:

Nabil Nassif, Jocelyne Erhel, Bernard Philippe, Introduction to Computational Linear Algebra, CRC press, 2015.

Sheldon Axler, Linear Algebra Done Right, Springer, 2014.

Gilbert Strang, “Linear Algebra for Learning Data”, Cambridge press, 2019.

Kenneth Hoffmann and Ray Kunze, Linear Algebra, Second Edition, Prentice Hall, 1971.

Mike Cohen, Practical Linear Algebra for Data Science, Oreilly Publisher, 2022.