Jacobi rotation
In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to zero a symmetric pair of off-diagonal entries of an n×n real symmetric matrix, A. It is the core operation in the Jacobi eigenvalue algorithm, which is numerically stable and well-suited to implementation on parallel processors . == Formulation == The Jacobi rotation is applied as a similarity transformation: A ↦ Q k ℓ T A Q k ℓ = A ′ .