LINEAR ALGEBRA
(Common to II Semester B.E and B.Tech Students)
  Module – I: Vector Spaces
Introduction to Vector Spaces, Examples, Subspaces, Linear
Combinations, Span, Generating Sets, Linear Dependence and
Independence, Basis and Dimension, Dimension of Subspaces.
Activities: Open-Source software, exercises to test linear dependence
and independence using rank, compute span and basis of a set of vectors,
determine the dimension of subspaces, and illustrate the concept of
subspace and basis in R2/R3 with visualization.
Module – II: Linear Transformations and Diagonalization
Null Space, range, Dimension Theorem (statement only), Matrix
representation of a linear transformation, Eigenvalues and Eigenvectors,
Diagonalizability.
Activities: Open-Source software, exercises to compute the matrix
representation of a linear transformation, find the null space and range of
a matrix, and compute eigenvalues and eigenvectors of a matrix.
Module – III: Inner Product Spaces
Inner product, Norms, Cauchy Schwarz inequality, Gram-Schmitdt
orthogonalization, Simple problems (upto R3).
Activities: Open-Source software, exercises to compute inner
products and vector norms.
Module – IV: Matrix Decomposition
Orthogonal transformation of a symmetric matrix to diagonal form –
Positive definite matrices, QR decomposition, Singular Value
Decomposition (SVD), Least squares solutions – simple problems (up to
3 × 3 matrices).
Activities: Open-Source software, exercises to check if a matrix is
positive definite, perform QR decomposition and SVD using built-in
functions.