Course curriculum

  • 1

    Chapter 1: Vector Spaces

    • Lecture 1 : Definition of Vector Space

    • Lecture 2 : Theorem 1

    • Lecture 3 : Examples Of Vector Space

    • Lecture 4 : Linear Combination, Example 1

    • Lecture 5 : Linear Combination, Examples 2,3,4

    • Lecture 6 : Spanning Set , Example 5

    • Lecture 7 : Example 6,7

    • Lecture 8 : Definition of Subspace, Theorem 1

    • Lecture 9 : Intersection of Subspaces, Theorem 2 and Theorem 3

    • Lecture 10 : Definition of Solution Space, Theorem4

    • Lecture 11 : Linear Span(Definition), Theorem 1

    • Lecture 12 : Theorem 2

    • Lecture 13 : Example 1,2

    • Lecture 14 : Linear Independence and dependence, Example 1

    • Lecture 15 : Example2,3

    • Lecture 16 : Theorem 1 (Linear Dependence)

    • Lecture 17 : Linear Independence And Echelon Form, Example 4

    • Lecture 18 : Definition of Basis, Theorem 1

    • Lecture 19 : Theorem 2

    • Lecture 20 : Theorem 3

    • Lecture 21 : Theorem 4, Assignments

    • Lecture 22 : Dimensions Of Vector Space, Example 1,2

    • Lecture 23 : Theorem 5

    • Lecture 24 : Theorem 6, Theorem 7, Assignment

    • Lecture 25 : Theorem 8

    • Lecture 27 : Basis Finding Algorithms 1 and 2, solved Example

    • Lecture 28 : Rowspace Of A Matrix, Finding Basis For Rowspace
  • 2

    Chapter 2 : Linear Mappings

    • Lecture 1 : Mapping , Inverse Image,Bijective Mapping, Matrix Mapiing (Matrix Representing a Mapping)

    • Lecture 2 : Linear Mapping, Example 1,2

    • Lecture 3 : Example 3,4,5 (linear Mapping)

    • Lecture 4 : Theorem 1

    • Lecture 5,6 : Kernel and Image of a Linear Mapping, Example-1,2,3

    • Lecture 7 : Theorem2, Theorem 3

    • Lecture 8,9 : Rank Nullity theorem (PU Annual 2017,2019,2020)
  • 3

    Chapter 3 : Eigenvalues and Eigenvectors, Diagonalization

    • Lecture 1 : Diagonalizable Matrix and Linear Operator, Example

    • Lecture 2 : Characteristics Polynomial of a Matrix, Use of Cayley Hamilton Theorem

    • Lecture 3,4 : Cayley-Hamilton th

    • Lecture 5,6 : Eigenvalues and Eigenvectors, with examples

    • Lecture 7,8 : Diagonalizing a matrix, with examples

    • Lecture 9, 10 : Diagonalizing a 3x3 matrix, PU Annual 2021

    • Lecture 11,12 : Theorem - Eigenvalues of symmetric matrices are always real (PU Annual 2017)

    • Lecture 13 : Theorem 2 - Eigenvectors vectors of a real Symmetric matrix corresponding to distinct Eigenvalues are orthogonal

    • Lecture 14 : Orthogonal matrix, Normalising a vector, Cauchy-Schwarz inequality

    • Lecture 15,16 : Orthogonal Diagnolization Algorithm example 1,2

    • Lectures 17,18 : Q1 PU Annual 2019,2020, Q 2 PU Annual 2017,2018