# The Jacobi Method for Real Symmetric Matrices

• H. Rutishauser
Chapter
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)

## Abstract

As is well known, a real symmetric matrix can be transformed iteratively into diagonal form through a sequence of appropriately chosen elementary orthogonal transformations (in the following called Jacobi rotations):
$${A_k} \to {A_{k + 1}} = U_k^T{A_k}{U_k}{\text{ (}}{A_0}{\text{ = given matrix),}}$$
where U k = U k(p,q, φ) is an orthogonal matrix which deviates from the unit matrix only in the elements
$${u_{pp}} = {u_{qq}} = \cos (\varphi ){\text{ and }}{u_{pq}} = - {u_{qp}} = \sin (\varphi ).$$

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