On matrix inverses modulo a subspace

✍ Scribed by Miguel V Carriegos; Ma Isabel Garcı́a-Planas

• Book ID: 104155561
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 188 KB
• Volume: 379
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00503-2

✦ Synopsis

Given a pair of matrices (A, B) ∈ R n×n × R n×m with coefficients in a commutative ring we study the problem of finding a matrix F such that A + BF becomes invertible.

We point out some relations between the problem of finding feedback inverses of A modulo B and the pole-shifting problem for the pair (A, B). In fact we give feedback invertibility results over a well known large class of rings related with the pole-shifting: the class of PA rings. On the other hand we also give a pointwise-global characterization. The ring R of rational integers and the coordinate ring of the real unit circle R[x, y]/(x 2 + y 2 -1) are studied in some detail. Finally the problem of derivative feedback standardization of generalized linear systems is reviewed as a particular case.