The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field
نویسندگان
چکیده
منابع مشابه
The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field
Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Z be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Z such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Z is an affine variety over an algebraically closed field.
متن کاملMultiplicative Complexity of Commutative Group Algebras over Algebraically Closed Fields
We determine structure and multiplicative complexity of commutative group algebras over algebraically closed fields. Commutative group algebra A of dimension n over algebraically closed field is isomorphic to B, where B is a superbasic algebra of minimal rank (see [5] for definition), and t is maximal that t | n, p t. Multiplicative and bilinear complexity of A equal to 2n − t.
متن کاملDecomposition of Homogeneous Polynomials over an Algebraically Closed Field
Let F be a homogeneous polynomial of degree d in m+ 1 variables defined over an algebraically closed field of characteristic zero and suppose that F belongs to the s-th secant varieties of the standard Veronese variety Xm,d ⊂ P( m+d d )−1 but that its minimal decomposition as sum of d-th powers of linear forms M1, . . . ,Mr is F = M 1 +· · ·+M r with r > s. We show that if s+r ≤ 2d+1 then such ...
متن کاملCovers of the multiplicative group of an algebraically closed field of characteristic zero
Model theoretically one can interprete the sequence as a structure in various ways. The simplest algebraic structure on the sequence which bears an interesting algebro-geometric information is the one with the additive group structure in the middle and with the full algebraic geometry on C. The latter is equivalent to treating C as C \ {0} with the full field structure on C. We call this struct...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
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: SIAM Journal on Matrix Analysis and Applications
سال: 2001
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479800378192