Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4147

 Title: A Note on Smooth Matrices of Constant Rank Authors: Ciampa, MaurizioVolpi, Aldo Keywords: Constant rankDoležal’s TheoremMatrices depending on a parameter Issue Date: 2005 Publisher: Università degli Studi di Trieste. Dipartimento di Matematica e Informatica Citation: Maurizio Ciampa, Aldo Volpi, "A Note on Smooth Matrices of Constant Rank", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 37 (2005), pp. 155-170. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics37 (2005) Abstract: We show that, given a $C^h$ time–varying matrix A(t) of constant rank, there exists a $C^h$ matrix H(t) such that the rows of H(t)A(t) are an orthonormal basis of the space spanned by the rows of A(t). We present some consequences of this result and, in particular, we prove a version for $m \times n$ matrices of Doležal's Theorem. These results are not new, and references are given. All the proofs of the results stated in these references, with the exception of those based on the use of differential equations — which holds only for $h \geq 1$ —, find suitable $C^h$ matrices defined on overlapping subsets of the domain and then patch them together without losing regularity and the other required properties. In our approach the patching needs to be done only for matrices consisting of one row and all the remaining results are obtained by usual algebraic tools. URI: http://hdl.handle.net/10077/4147 ISSN: 0049-4704 MS Classification: 15A54 Appears in Collections: Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.37 (2005)

Files in This Item:

File Description SizeFormat