Displaying similar documents to “The control problem x ˙ = ( A ( 1 - u ) + B u ) x : A comment on an article by J. Kučera”

Infinite elementary divisor structure-preserving transformations for polynomial matrices

Nicholas Karampetakis, Stavros Vologiannidis (2003)

International Journal of Applied Mathematics and Computer Science

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The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where...

Generating functions and Bézoutians

Vlastimil Pták (1996)

Mathematica Bohemica

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Using the idea of the generating function of a matrix in an extended sense we establish a Bezoutian type formula for a matrix M satisfying an intertwining relation of the form M A T = A M . In the particular case of classical generating functions this formula gives a simple proof of Lander’s theorem on the inverse of a Hankel matrix.