Matrix Computation and its applications
https://www.youtube.com/playlist?list=PLp6ek2hDcoNDjDTiFlWp-Lx0XshPvX1tR
2021.10.17
视频选集
（45/59）
INTRO
04:59
Binary Operation and Groups
32:35
Vector Spaces
32:44
Some Example of Vector Spaces
33:34
Some Example of Vector Spaces (contd)
32:07
Subspace of a Vector Space
33:14
Spanning Set
31:21
Properties of Subspace
33:44
Properties of Subspace (contd)
33:57
Linearly independent and dependent vectors
34:28
Linearly independent and dependent vectors (contd)
33:26
Properties of linearly independent and dependent vectors
34:16
Properties of linearly independent and dependent vectors (contd)
33:53
Basis and Dimension of a Vector Space
34:33
Examples of Basis and standard basis of a vector space
33:03
Linear Functions
33:42
Range space of a matrix and row reduced echelon form
36:09
Row equivalent matrices
32:26
Row equivalent matrices (contd)
32:23
Null Space of a Matrix
34:26
Four subspaces associated with a given matrix
33:18
Four subspaces associated with a given matrix (contd)
38:28
Linear Independence of the rows and columns of a matrix
32:14
Application of diagonal dominant matrices
37:30
Application of Zero Null space Interpolating polynomial and wronskian matrix
36:49
Characterization of basis of a vector space and its subspaces
44:37
Coordinate of a vector with respect to ordered basis
32:24
Examples of different subspaces of a vector space of polynomials having degree l
42:31
Linear transformation
33:51
Properties of linear transformation
38:44
Determining linear transformation on a vector space by its value on the basis el
33:59
Rank and nuility of a linear transformation
34:00
Rank-nuility theorem
38:53
Range space and null space of a linear transformation
32:18
Application of rank-nuility theorem and inverse of a linear transformation
35:45
Matrix associated with linear transformation
35:05
Matrix representation of a linear transformation relative to ordered bases
36:56
Matrix representation of a linear transformation relative to ordered bases (cont
36:58
Linear map associated with a matrix
34:13
Similar matrices and diagonalisation of matrix
41:49
Orthogonality of the four subspaces associated with a Matrix
42:16
Gram-Schmidt orthogonalisation process
44:01
QR factorisation
32:52
Inner Product Spaces
43:04
Inner product on different real vector spaces and basis of complex vector space
54:13
Inner product on complex vector spaces and Cauchy-Schwarz inequality
59:14
Norm of a vector
46:25
Matrix norm
01:00:59
Sensitivity analysis of a system of linear equations
56:48
Orthonormal bases of a vector space
41:40
Best approximation Least square method
01:03:34
Best approximation Least square method (contd)
54:38
Jordan-Canonical Form
46:17
Some examples on the Jordan form of a given matrix and generalised eigenvectors
46:44
Singular value decomposition (SVD) theorem
57:10
Matlab Octave code for solving SVD
32:56
Pseudo-inverseMoore-Penrose inverse
01:04:12
Householder transformation
47:03
MatlabOctave code for Householder transformation
48:17
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