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Jacobi and Givens Rotation Methods
This chapter is devoted to the application of plane rotations in the solution of the eigenvalue problem of symmetric matrices. After a brief introduction to the concept of rotation matrices, we study the iterative Jacobi rotation method for diagonalization and the Givens rotation method for tridiagonalization.
Plane Rotations
Figure 10.1: Rotation of axes and change of basis
Consider a point P(x, y) in the xy-plane. If the coordinate axes undergo a clockwise rotation through an angle ϕ about the origin and the new coordinates of P with respect to the changed axes X′Y′ become (x′,y′), then from Fig. 10.1 ...
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