Matrix Computation and its applications HDXYBF0DMW

URI	`m2://res/HDXYBF0DMW`
Kind	course
Creators	Mani Mehra (instructor), Vivek Kumar Aggarwal (instructor)
Date	2021-07-21
Scope	in
Ids	course 049tgcd06:111102152

Expressions

e1: edition

Language	en
Date	2021-07-21

m1: page, IIT Delhi (record). nptel 111102152
m2: page, 2021-07-21 (record). nptel 111102152

Contents

part 1: Week 1
session 1: Binary Operation and Groups
session 2: Vector Spaces
session 3: Some Example of Vector Spaces
session 4: Some Example of Vector Spaces (contd.)
session 5: Subspace of a Vector Space
session 6: Spanning Set
part 2: Week 2
session 7: Properties of Subspace
session 8: Properties of Subspace (contd.)
session 9: Linearly independent and dependent vectors
session 10: Linearly independent and dependent vectors (contd.)
session 11: Properties of linearly independent and dependent vectors
session 12: Properties of linearly independent and dependent vectors (contd.)
part 3: Week 3
session 13: Basis and Dimension of a Vector Space
session 14: Examples of Basis and standard basis of a vector space
session 15: Linear Functions
session 16: Range space of a matrix and row reduced echelon form
session 17: Row equivalent matrices
session 18: Row equivalent matrices (contd.)
part 4: Week 4
session 19: Null Space of a Matrix
session 20: Four subspaces associated with a given matrix
session 21: Four subspaces associated with a given matrix (contd.)
session 22: Linear Independence of the rows and columns of a matrix
session 23: Application of diagonal dominant matrices
session 24: Application of Zero Null space: Interpolating polynomial and wronskian matrix
part 5: Week 5
session 25: Characterization of basis of a vector space and its subspaces
session 26: Coordinate of a vector with respect to ordered basis
session 27: Examples of different subspaces of a vector space of polynomials having degree less than or equal to 3
session 28: Linear transformation
session 29: Properties of linear transformation
session 30: Determining linear transformation on a vector space by its value on the basis element
part 6: Week 6
session 31: Range space and null space of a linear transformation
session 32: Rank and nuility of a linear transformation
session 33: Rank-nuility theorem
session 34: Application of rank-nuility theorem and inverse of a linear transformation
session 35: Matrix associated with linear transformation
session 36: Matrix representation of a linear transformation relative to ordered bases
part 7: Week 7
session 37: Matrix representation of a linear transformation relative to ordered bases (contd.)
session 38: Linear map associated with a matrix
session 39: Similar matrices and diagonalisation of matrix
session 40: Orthonormal bases of a vector space
part 8: Week 8
session 41: Gram-Schmidt orthogonalisation process
session 42: QR factorisation
session 43: Inner Product Spaces
session 44: Inner product on different real vector spaces and basis of complex vector space
part 9: Week 9
session 45: Inner product on complex vector spaces and Cauchy-Schwarz inequality
session 46: Norm of a vector
session 47: Matrix norm
session 48: Sensitivity analysis of a system of linear equations
part 10: Week 10
session 49: Orthogonality of the four subspaces associated with a Matrix
session 50: Best approximation : Least square method
session 51: Best approximation : Least square method (contd.)
session 52: Jordan-Canonical Form
part 11: Week 11
session 53: Some examples on the Jordan form of a given matrix and generalised eigenvectors
session 54: Singular value decomposition (SVD) theorem
session 55: Matlab / Octave code for solving SVD
part 12: Week 12
session 56: Pseudo-inverse/Moore-Penrose inverse
session 57: Householder transformation
session 58: Matlab/Octave code for Householder transformation

Catalogue records

nptel: 111102152 (manifestation)
nptel_video: 111102152 (manifestation)