Jacobi eigenvalue algorithm

In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). It is named after Carl Gustav Jacob Jacobi, who first proposed the method in 1846, but only became widely used in the 1950s with the advent of computers.

Let ${\displaystyle S}$ be a symmetric matrix, and ${\displaystyle G=G(i,j,\theta )}$ be a Givens rotation matrix. Then:

is symmetric and similar to ${\displaystyle S}$.

...
Wikipedia