Antoulas, A.C.Sorensen, D.C.2018-06-182018-06-182000-05Antoulas, A.C. and Sorensen, D.C.. "Lyapunov, Lanczos, and Inertia." (2000) <a href="https://hdl.handle.net/1911/101942">https://hdl.handle.net/1911/101942</a>.https://hdl.handle.net/1911/101942We present a new proof of the inertia result associated with Lyapunov equations. Furthermore we present a connection between the Lyapunov equation and the Lanczos process which is closely related to the Schwarz form of a matrix. We provide a method for reducing a general matrix to Schwarz form in a finite number of steps (O(n3)). Hence, we provide a finite method for computing inertia without computing eigenvalues. This scheme is unstable numerically and hence is primarily of theoretical interest.12 ppengTechnical reportTR00-13