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My name is Abhishek Agrawal. I am a grad student in Computer Science. I know very little about scalar equations. But my research has led me to them and I am at my wits end on how to go about solving them. I have looked around every where but I am unable to start.

1. The problem statement, all variables and given/known data

http://en.wikipedia.org/wiki/Divide-and-conquer_eigenvalue_algorithm

This is a Wikipedia link on how to use the divide and conquer algorithm to solve for eigen values of a matrix. I understood most of the stuff but towards the end of the link, the author ends up with this equation

1 + wT(D − λI)−1 w = 0

which is a scalar equation. He transforms this equation into an another form. (The formatting came bad on this post, better to view it in Wiki)

1 + \sum_{j=1}^{m} \frac{w_{j}^{2}}{d_{j} - \lambda} = 0.

What I cannot understand is how is the summation applied. How does the author get the wj and dj terms from the matrix . Is he using an entire row or is there some thing I am missing ?

I would appreciate if some one could give me some links so as to what I am missing or could point me to some tutorials

Any help would be appreciated

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# Homework Help: Scalar Equations: How to solve them

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