On the convergence of the classical Jacobi method for real symmetric matrices with non-distinct eigenvalues

Among hollow, symmetric $n$-by-$n$ nonnegative matrices, it is shown that any number $k$, $2\leq k\leq n-1$ of nonpositive eigenvalues is possible. However, as $n$ grows, small numbers of nonpositive eigenvalues become increasingly rare. In particular, if ...

We consider the class of totally nonnegative (TN) matrices---matrices all of whose minors are nonnegative. Any nonsingular TN matrix factors as a product of nonnegative bidiagonal matrices. The entries of the bidiagonal factors parameterize the set of ...

Computing all eigenvalues of a modest size matrix typically proceeds in two phases. In the first phase, the matrix is transformed to a suitable condensed matrix format, sharing the eigenvalues, and in the second stage the eigenvalues ...