Regression Model Report

1
Machine Learning
Student Name
Institution
State
1. Let,
S= [ cos α sin α
−sin α cos α ]
a. Orthogonal matrix is a matrix such
that; S ST =I where I is the identity
matrix.
Let α be 300
S= [ cos 30 sin 30
−sin 30 cos 30 ]= [ 0.866 0.5
−0.5 0.866 ]
S ST =
[0.866 0.5
−0.5 0.866 ][0.866 −0.5
0.5 0.866 ]
S ST =[ 0.5 0
0 0.5 ]
S ST =0.5 [1 0
0 1 ]
Since we can easily get identity matrix,
matrix S is orthogonal
b. 2 X 2 Symmetric matrix
A=
[a11 a12
a21 a22 ]
Let A=
[ 4 3
3 2 ]
∴ tan 2 α =6
2 =3
2 α=tan−1 3
2 α=71.5 60
α =35.7 80
B=¿
[ cos 35.78 sin35.78
−sin 35.78 cos 35.78 ][4 3
3 2 ][cos 35.78 −sin35.78
sin 35.78 cos 35.78 ]
B=¿ [ 0.81 0.58
−0.58 0.81 ][ 4 3
3 2 ][ 0.81 −0.58
0.58 0.81 ]
B= [ 4.98 3.59
0.11 −0.12 ][ 0.81 −0.58
0.58 0.81 ] =
[ 6.12 0.0
0.0 −0.13 ]