Matrix cyclization over complex polynomials

✍ Scribed by Wiland Schmale

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 673 KB
• Volume: 275-276
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)10030-1

✦ Synopsis

Let A be an n x n, B an n x tn complex polynomial matrix. The following open problem is investigated: does there exist a complex polynomial (m x n)-matrix F such that A + BF has a cyclic vector in the image of B? An explicit solution of the problem is given for the following generic situation: n 2 4, [B, AB, . , A"-'B] is rightinvertible (necessary), the entries of a specific normalized form of (A, B) do not satisfy certain polynomial equations, and one specific entry has at least one simple zero outside a certain finite set. The exceptional equations are given explicitely and can easily be checked for.