Characterizing the existence of local smith forms for C-infinity families of matrix operators - Lopez-Gomez, J; Mora-Corral, C (2003)
This paper characterizes whether or not the lengths of all Jordan chains of an arbitrary C-infinity family of square matrices L(lambda) are uniformly bounded from above. Consequently, the problem of ascertaining whether or not a local Smith form at a given singular value -eigenvalue- lambda(0) of L(lambda) exists is solved. Actually, a local Smith form exists if and only if lambda(0) is an algebraic eigenvalue of L(lambda) The main technical tools to obtain this characterization are the construction of the local Smith form of P. J. Rabier [8], and the transversalization theory of J. Esquinas and J. Lopez-Gomez [3, 2, 1, 6].