Week 10 Flashcards
1
Q
Solve EigenValue problem analytically
A
(A - λI)x = 0
Requiring that |A-λI| = 0 we have that the expansion of determinants leads to the polynomial equation (characteristic)
For which the roots are the EVs
2
Q
Jacobi Method (idea)
A
Require that A is symmetric
We can take any non singular matrix P and replace x with Px*
This is repeated using rotation matrices
3
Q
General Form of Jacobi rotation matrix
A
4
Q
To find θ for element Akl* to equal 0
A
Where A* = R-1AR
We have
5
Q
Cos(0)
A
1
6
Q
Cos(π)
A
-1
7
Q
Cos(π/2)
A
0
8
Q
Sin(0)
A
0
9
Q
Sin(π)
A
0
10
Q
Sin(π/2)
A
1
