𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The number of nonconstant invariant polynomials of matrices with several prescribed blocks

✍ Scribed by Glória Cravo; Fernando C. Silva

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
107 KB
Volume
368
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

Consider a n × n matrix partitioned into k × k blocks: C = [C i,j ], where C 1,1 , . . . , C k,k are square. This paper studies the possible numbers of nonconstant invariant polynomials of C when a diagonal of blocks C i,j is fixed and the others vary.

📜 SIMILAR VOLUMES

The number of invariant polynomials of a
The number of invariant polynomials of a matrix with prescribed off-diagonal blocks
✍ Maria da Graça Marques 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 323 KB

Let A be an n × n matrix over an arbitrary field F of the form AI, 1 AI, z] A = A2.1 A2,2 J, where A1, 1 ~ F p×p, A2. 2 ~ F q×q, and p + q = n. We characterize the possible nmnber of nontrivial invariant polynomials of A, when the submatrices A L 2 and A2, 1 are prescribed.

On the characteristic polynomial of matr
On the characteristic polynomial of matrices with prescribed rows
✍ Susana Furtado; Fernando C. Silva 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 228 KB

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 fac