Jacobi Rotation Matrix

A Matrix used in the Jacobi Transformation method of diagonalizing Matrices. It contains $\cos\phi$ in $p$ rows and columns and $\sin\phi$ in $q$ rows and columns,

$$P_{pq} \equiv \left[{\matrix{ 1 & & & & & & & & 0\cr & \ddot... ...& & \vdots & & & \ddots & \cr 0 & & & & & & & & 1\cr}}\right].$$

See also Jacobi Transformation

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Jacobi Transformation of a Symmetric Matrix.'' §11.1 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 456-462, 1992.