Eigenvalues and Eigenvectors

This module introduces eigen values and vectors analytically and graphically with engineering relevance. Rayleigh’s power method is discussed in detail with merits and demerits. Significant number of model questions paper problems have been solved to give a comprehensive understanding of the examiner’s perspective.

Salient features of this module are:

• Pre-requisites to Fundamental Matrix Theory
• Graphical visualization
• Concept testing
• Unravelling examiners mind
• Model question paper

Course Contents: 

Pre-requisites to Matrix Algebra and Rank

• Types of Matrices
  • Types of Matrices – Part 1
  • Types of Matrices – Part 2
  • Types of Matrices – Part 3
• Understanding Determinant
  • Determinant of a 3×3 matrix
  • Determinant of a 4×4 matrix
• Vector Algebra for Matrix Multiplication
  • Dot and Cross Product – Part 1
  • Dot and Cross Product – Part 2
• Graphical Perspection of a Determinant
  • Perspective – 1
  • Perspective – 2
• Inverse of a Matrixe
  • Introduction – 2X2 – Matrix
  • Example – 2X2 – Matrix
  • General procedure and Incidental facts – 3X3 Matrix
  • Observations
  • Applications
• Matrix-Vector Multiplication
  • Introduction – Perspective 1 – Linear Algebra
  • Introduction – Perspective 2 – Linear Algebra
  • Quiz 1
  • Quiz 2
  • Quiz 3
• Matrix-Matrix Multiplication
  • Introduction – Perspective – Linear Algebra
  • Introduction – Alternate Method
  • Quiz 1
  • Quiz 2
  • Quiz 3
  • Quiz 4
  • Quiz 5

Eigenvalues and Eigenvectors

• • Introduction
  • Graphical Understanding of Eigenvalues and Eigenvectors
  • Understanding Eigen values – 2×2 matrix
  • Eigen values – Observations
  • Eigen values – Example
  • Deriving Eigen vectors – 2×2 matrix
  • Eigen vectors – Observations
  • Deriving Eigen value and vectors – 3×3 matrix
  • Rayleigh’s Power Method – (Conceptual Understanding)
  • Rayleigh’s Power Method – Problems: (Problem 1)
  • Rayleigh’s Power Method – Problems: (Problem 2)
  • Rayleigh’s Power Method – (Conceptual Understanding of Rate of Convergence)