The Classical Jacobi Algorithm
Introduction | The Jacobi eigenvalue algorithm | Parallel revival | Purpose of this package | Brief synopsis of the algorithm | Let $S$ be a $2\times2$ symmetric matrix, with entries $s_{ij}$. It it well known that any symmetric matrix may be diagonalized by an orthogonal similarity transformation. In symbols, for this special case, this implies we need to choose a value for $\theta$ for which:$$ H^{\mathsf{T}} S H =\left[\begin{array}{lr}\cos \theta & -\sin \theta \\sin \theta & \cos \theta\end{array} \right]\left[\begin{array}{lr}s_{11} & s_{12} \s_{21} & s_{22}\end{array} \right]\left[\begin{array}{rr}\cos \theta & \sin \theta \-\sin \theta & \cos \theta\end{array} \right] | Stagewise protocol | Examples | Code | R | Rcpp