These values are invariant under similarity transformations, and Schur's inequalities relate these values to the entries of the   matrix from which they are calculated.
The Gershgorin Circle Theorem guarantees that each of these will be con- tained in a certain set of disks. The Lanczos algorithm is used to compute these non-vector quantities, and Lyapunov's First Theorem gives necessary and su cient conditions to ensure that the real parts of these quantities will be neg- ative. These values are invariant under similarity transformations, and Schur's inequalities relate these values to the entries of the   matrix from which they are calculated. These values are also known as characteristic roots because they are the roots of a matrix's characteristic polynomial. For ten points, identify these scalars associated with a matrix and corresponding to vectors with the same pre x.
The Gershgorin Circle Theorem guarantees that each of these will be con- tained in a certain set of disks.
eigenvalues [accept characteristic roots before read, accept characteristic values, accept proper values, accept latent roots]