𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The number of invariant polynomials of a matrix with prescribed off-diagonal blocks

✍ Scribed by Maria da Graça Marques

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
323 KB
Volume
258
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

The number of nonconstant invariant poly
The number of nonconstant invariant polynomials of matrices with several prescribed blocks
✍ Glória Cravo; Fernando C. Silva 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 107 KB

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.

On the number of invariant polynomials o
On the number of invariant polynomials of matrix commutators
✍ Enide Andrade Martins; Fernando C. Silva 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 534 KB

We study the possible numbers of noneonstant invariant polynomials of the matrix commutator XA -AX, when X varies.