# QR factorization- Eigen values

1. Jan 24, 2012

### svishal03

I'm attempting to write a code for computing the Eigen values of a real symmetric matrix and I'm using the QR algorithm.I'm referring wiki,Numerical Recipees book and other web serach articles.

This is a part of the self-study course I'm doing in Linear Algebra to upgrde my skills.

My aim is not only getting the algorithm but also understanding Linear algebra and this site is a great help.

As I conclude, following algorithm is being planned by me for implemantation:

1. First and foremost carry out Householder transformation to obtain a tridiagonal matrix from (n-2) householder iterations where n is the size of the square symmetric matrix.

2. During each of the above n-2 iterations, we have Q1,Q2,Q3…..Q(n-2) Householdr matrices

3. We can now obtain Q and R (of QR factorization) where Q is an orthogonal matrix and R is an upper triangular matrix

4. R = Qn-2* Qn-1*……….*Q2*Q1

5. Q = Q1*Q2*………*Qn-2

6. Thus we decompose the original matrix A into A = QR

Am I right above?

I'm not very clear how to get Eigen values following this.Can anyone site a good refernce?

Vishal

2. Jan 26, 2012

### svishal03

Please can anyone help, it is very urgent..