For a real symmetric matrix A of size n x n, the Jacobian Eigenvalue Algorithm produces
- n - Eigen values of A in the form of a Square Diagonal Eigenvalue Matrix of order n
- n - Eigen vectors of A corresponding to each of the n-Eigen values of A in the form of a n x n Matrix with columns as Eigen vectors.
Also, a matrix is said to be positive definite if it’s symmetric and all its eigenvalues are non-negative i.e. every Eigenvalue > 0.
Does the Jacobi Eigenvalue algorithm guarantees producing a positive definite Eigenvalue diagonal matrix for every real symmetric matrix A ?
If the answer to above queestion is no, then
- What must be changed so that Jacobi algorithm guarantees producing a positive definite Eigenvalue diagonal matrix ?
- If Jacobi Algorithm cannot guarantee that, are there any alternative iterative methods that produce n-Eigenvalues and n-Eigen vectors but guarantee producing a positive definite Eigenvalue matrix ?