Matrices with prescribed characteristic polynomial and principal blocks
نویسندگان
چکیده
منابع مشابه
On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems
Let A 2 F , B 2 F , where F is an arbitrary eld. In this paper, the possible characteristic polynomials of [A B ], when some of its columns are prescribed and the other columns vary, are described. The characteristic polynomial of [A B ] is de ned as the largest determinantal divisor (or the product of the invariant factors) of [xIn A B ]. This result generalizes a previous theorem by H. Wimmer...
متن کاملCounting Integral Matrices with a given Characteristic Polynomial
We give a simpler proof of an earlier result giving an asymptotic estimate for the number of integral matrices, in large balls, with a given monic integral irreducible polynomial as their common characteristic polynomial. The proof uses equidistributions of polynomial trajectories on SL(n, R)/SL(n, Z), which is a generalization of Ratner’s theorem on equidistributions of unipotent trajectories....
متن کاملThe Enhanced Principal Rank Characteristic Sequence for Hermitian Matrices
The enhanced principal rank characteristic sequence (epr-sequence) of an n×n matrix is a sequence `1`2 · · ·`n, where each `k is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been ma...
متن کاملThe Characteristic Polynomial of Some Perturbed Tridiagonal k-Toeplitz Matrices
We generalize some recent results on the spectra of tridiagonal matrices, providing explicit expressions for the characteristic polynomial of some perturbed tridiagonal k-Toeplitz matrices. The calculation of the eigenvalues (and associated eigenvectors) follows straightforward. Mathematics Subject Classification: 15A18, 42C05, 33C45
متن کاملMatrices with Prescribed Row and Column Sums
This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1981
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500016527