Math 2.0

Resources / course

Matrix Analysis with Applications ZQDCBNVGVV

URIm2://res/ZQDCBNVGVV
Kindcourse
CreatorsSanjeev Kumar (instructor), S. K. Gupta (instructor)
Date2018-07-17
Scopein
Idscourse 00582g326:111107112

Expressions

e1: edition

Languageen
Date2018-07-17
Contents
  • part 1: Week 1
  • session 1: Elementary row operations
  • session 2: Echelon form of a matrix
  • session 3: Rank of a matrix
  • session 4: System of Linear Equations-I
  • session 5: System of Linear Equations-II
  • part 2: Week 2
  • session 6: Introduction to Vector Spaces
  • session 7: Subspaces
  • session 8: Basis and Dimension
  • session 9: Linear Transformations
  • session 10: Rank and Nullity
  • part 3: Week 3
  • session 11: Inverse of a Linear Transformation
  • session 12: Matrix Associated with a LT
  • session 13: Eigenvalues and Eigenvectors
  • session 14: Cayley-Hamilton Theorem and Minimal Polynomial
  • session 15: Diagonalization
  • part 4: Week 4
  • session 16: Special Matrices
  • session 17: More on Special Matrices and Gerschgorin Theorem
  • session 18: Inner Product Spaces
  • session 19: Vector and Matrix Norms
  • session 20: Gram Schmidt Process
  • part 5: Week 5
  • session 21: Normal Matrices
  • session 22: Positive Definite Matrices
  • session 23: Positive Definite and Quadratic Forms
  • session 24: Gram Matrix and Minimization of Quadratic Forms
  • session 25: Generalized Eigenvectors and Jordan Canonical Form
  • part 6: Week 6
  • session 26: Evaluation of Matrix Functions
  • session 27: Least Square Approximation
  • session 28: Singular Value Decomposition
  • session 29: Pseudo-Inverse and SVD
  • session 30: Introduction to Ill-Conditioned Systems
  • part 7: Week 7
  • session 31: Regularization of Ill-Conditioned Systems
  • session 32: Linear Systems : Iterative Methods I
  • session 33: Linear Systems : Iterative Methods II
  • session 34: Non-Stationary Iterative Methods: Steepest Descent-I
  • session 35: Non-Stationary Iterative Methods: Steepest Descent-II
  • part 8: Week 8
  • session 36: Krylov Subspace Iterative Methods (Conjugate Gradient Method)
  • session 37: Krylov Subspace Iterative Methods (CG and Pre-Conditioning)
  • session 38: Introduction to Positive Matrices
  • session 39: Non-Negativity and Irreducible Matrices
  • session 40: Polar Decomposition

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