On the characteristic polynomial of matrices with prescribed rows

✍ Scribed by Susana Furtado; Fernando C. Silva

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 228 KB
• Volume: 293
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00020-8

✦ Synopsis

Let e P p nÂn , f P p nÂt , where F is an arbitrary ®eld. We describe the possible characteristic polynomials of e f, when some of its rows are prescribed and the other rows vary. The characteristic polynomial of e f is de®ned as the largest determinantal divisor (or the product of the invariant factors) of xs n À e À f. This result generalizes a previous theorem by H. Wimmer [Monasth. Math. 78 (1974) 256±263], which studies the same problem when t 0.