New inverse data for tridiagonal matrices

We introduce bidiagonal coordinates, a new set of spectral coordinates on open dense charts covering the space of real symmetric tridiagonal matrices of simple spectrum. In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, reduced tridiagonal matrices now lie in the interior of some chart. Bidiagonal coordinates yield therefore an explicit atlas for TΛ, the manifold of real tridiagonal matrices with given spectrum Λ. These new coordinates are convenient for the study of asymptotics of isospectral dynamics, both for continuous and discrete time.