O'Reilly logo

Applied Mathematical Methods by Bhaskar Dasgupta

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

10

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 XY′ become (x′,y′), then from Fig. 10.1 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required