Matrix Computation and its applications
59 videos • 15,549 views • by IIT Delhi July 2018
1
INTRO
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2
Binary Operation and Groups
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3
Vector Spaces
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4
Some Example of Vector Spaces
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5
Some Example of Vector Spaces (contd.)
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6
Subspace of a Vector Space
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7
Spanning Set
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8
Properties of Subspace
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9
Properties of Subspace (contd.)
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10
Linearly independent and dependent vectors
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11
Linearly independent and dependent vectors (contd.)
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12
Properties of linearly independent and dependent vectors
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13
Properties of linearly independent and dependent vectors (contd.)
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14
Basis and Dimension of a Vector Space
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15
Examples of Basis and standard basis of a vector space
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16
Linear Functions
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17
Range space of a matrix and row reduced echelon form
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18
Row equivalent matrices
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19
Row equivalent matrices (contd.)
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20
Null Space of a Matrix
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21
Four subspaces associated with a given matrix
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22
Four subspaces associated with a given matrix (contd.)
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23
Linear Independence of the rows and columns of a matrix
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24
Application of diagonal dominant matrices
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25
Application of Zero Null space: Interpolating polynomial and wronskian matrix
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26
Characterization of basis of a vector space and its subspaces
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27
Coordinate of a vector with respect to ordered basis
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28
Examples of different subspaces of a vector space of polynomials having degree less than or equal 3
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29
Linear transformation
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30
Properties of linear transformation
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31
Determining linear transformation on a vector space by its value on the basis element
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32
Range space and null space of a linear transformation
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33
Rank and nuility of a linear transformation
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34
Rank-nuility theorem
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35
Application of rank-nuility theorem and inverse of a linear transformation
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36
Matrix associated with linear transformation
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37
Matrix representation of a linear transformation relative to ordered bases
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38
Matrix representation of a linear transformation relative to ordered bases (contd.)
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39
Linear map associated with a matrix
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40
Similar matrices and diagonalisation of matrix
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41
Orthonormal bases of a vector space
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42
Gram-Schmidt orthogonalisation process
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43
QR factorisation
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44
Inner Product Spaces
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45
Inner product on different real vector spaces and basis of complex vector space
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46
Inner product on complex vector spaces and Cauchy-Schwarz inequality
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47
Norm of a vector
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48
Matrix norm
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49
Sensitivity analysis of a system of linear equations
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50
Orthogonality of the four subspaces associated with a Matrix
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51
Best approximation : Least square method
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52
Best approximation : Least square method (contd.)
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53
Jordan-Canonical Form
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54
Some examples on the Jordan form of a given matrix and generalised eigenvectors
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55
Singular value decomposition (SVD) theorem
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56
Matlab / Octave code for solving SVD
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57
Pseudo-inverse/Moore-Penrose inverse
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58
Householder transformation
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59
Matlab/Octave code for Householder transformation
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