Invariant subspace, determinant and characteristic polynomials
نویسندگان
چکیده
منابع مشابه
Invariant subspace , determinant and characteristic polynomials ∗
Making use of an elementary fact on invariant subspace and determinant of a linear map and the method of algebraic identities, we obtain a factorization formula for a general characteristic polynomial of a matrix. This answers a question posed in [A. Deng, I. Sato, Y. Wu, Characteristic polynomials of ramified uniform covering digraphs, European Journal of Combinatorics 28 (2007), 1099–1114]. T...
متن کاملCharacteristic Polynomials of Subspace Arrangements and Finite Fields
Let A be any subspace arrangement in R defined over the integers and let Fq denote the finite field with q elements. Let q be a large prime. We prove that the characteristic polynomial /(A, q) of A counts the number of points in Fq that do not lie in any of the subspaces of A, viewed as subsets of Fq . This observation, which generalizes a theorem of Blass and Sagan about subarrangements of the...
متن کاملCharacteristic Polynomials
Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...
متن کاملCharacteristic and Ehrhart Polynomials
Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...
متن کاملCharacteristic polynomials and pseudospectra
In this paper, we study the ε-lemniscate of the characteristic polynomial in relation to the pseudospectrum of the associated matrix. It is natural to investigate this question because these two sets can be seen as generalizations of eigenvalues. The question of numerical determination of the ε-lemniscate raises the problem of computing the characteristic polynomial p. We can express the coeffi...
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: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.10.014