Week 8 (cont.)#
Lecturer: G Venkiteswaran, Faculty for BITS Pilani
Date: 19/Sep/2021
Topics Covered#
Inner Product Spaces#
Orthogonality#
Gram Schmidt Orthogonalization Process#
QR Decomposition#
Transformation of circle under matrix operation#
A = [1 2; 3 4]
%{
A =
1 2
3 4
}%
x1 = [1 2]'
%{
x1 =
1
2
}%
x2 = [-2 1]'
%{
x2 =
-2
1
}%
y1 = A * x1
%{
y1 =
5
11
}%
y2 = A * x2
%{
y2 =
0
-2
}%
Singular Value Decomposition#
Evaluation of U and V#
See notebook
Comparison between Eigenvalue decomposition and SVD#
Left and right singular matrix#
Summation form of SVD#
Face Recognition#
Average Faces#
Eigen Faces#
Image Keys#
Dimensionality Reduction#
