Question

I am trying to find eigenvalues (4,4,2) of the matrix
{{1,3,-3},{-3,7,-3},{-6,6,2}} by QR factorisation. It does not converge in 80,000 iterations.

Answer 1

What's QT factorization?

Answer 2

Is that the same as LU?

Answer 3

Romero, QR is not the same as LU. Q is orthogonal (QtQ=I) ann R is upper triangle.

Answer 4

To find the orthogal matrix you must find the unit vector of each column.

Answer 5

For upper right triangle reduce to echelon form.

Answer 6

Omitting the rule of having zeros above a pivot point.

Answer 7

Not sure how you can use it to find the eigen values.

Answer 8

Romero, see Strang's Linear Algebra page 364. In the nut-shell: in each iteration k
A(k) = Q(k)*R(k); A(k+1)= R(k)*Q(k)

Answer 9

Don't use that book. I use David c. Lay. I'll read my section see if I can help you later.

Answer 10

Correction. I am trying to find eigenvalues of the matrix
{{1,3,-3},{-3,7,-5},{-6,6,0}} by QR factorisation. It does not converge in 80,000 it…

Answer 11

is Q orthoGonal? or orthoNormal?

Answer 12

http://tutorial.math.lamar.edu/Classes/LinAlg/QRDecomposition.aspx

says Q is orthoN

Answer 13

first step I see than is to make this orthoNormal by checking making orthoGonal and unit up the vectors

Answer 14

Please ignore my previous messages.

The matrix in question has 2 complex eigenvalues (2+2.83i, 2-2.831) as well as the single real eigenvalue 4.