On the number of invariant polynomials of the product of matrices with prescribed similarity classes
โ Scribed by Yu Lin Zhang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 552 KB
- Volume
- 277
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
Consider a n ร n matrix partitioned into k ร 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.
Let A be an n ร n matrix over an arbitrary field F of the form AI, 1 AI, z] A = A2.1 A2,2 J, where A1, 1 ~ F pรp, A2. 2 ~ F qรq, 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.
Let e P p nรn , f P p nรt , where F is an arbitrary ยฎeld. 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 deยฎned as the largest determinantal divisor (or the product of the invariant fac
We study the possible numbers of noneonstant invariant polynomials of the matrix commutator XA -AX, when X varies.