Jacobi Transformation

A method of matrix diagonalization using Jacobi rotation matrices P_(pq). It consists of a sequence of orthogonal similarity transformations of the form


each of which eliminates one off-diagonal element. Each application of P_(pq) affects only rows and columns of A, and the sequence of such matrices is chosen so as to eliminate the off-diagonal elements.

See also

Jacobi Method, Jacobi Rotation Matrix

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Gentle, J. E. "Givens Transformations (Rotations)." §3.2.5 in Numerical Linear Algebra for Applications in Statistics. Berlin: Springer-Verlag, pp. 99-102, 1998.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.

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Jacobi Transformation

Cite this as:

Weisstein, Eric W. "Jacobi Transformation." From MathWorld--A Wolfram Web Resource.

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