Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials
نویسندگان
چکیده
منابع مشابه
Constructing all self-adjoint matrices with prescribed spectrum and diagonal
The Schur-Horn Theorem states that there exists a self-adjoint matrix with a given spectrum and diagonal if and only if the spectrum majorizes the diagonal. Though the original proof of this result was nonconstructive, several constructive proofs have subsequently been found. Most of these constructive proofs rely on Givens rotations, and none have been shown to be able to produce every example...
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Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...
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Necessary and sufficient conditions are proven for the existence of a square matrix, over an arbitrary field, such that for every principal submatrix the sum of the elements in the row complement of the submatrix is prescribed. The problem is solved in the cases where the positions of the nonzero elements of A are contained in a given set of positions, and where there is no restriction on the p...
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In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix. They perform this feat by applying a sequence of (N − 1) or fewer plane rotations, where N is the dimension of the matrix. Both the Bendel–Mickey and the Chan–Li algorithms are special c...
متن کاملConstructing Irreducible Polynomials with Prescribed Level Curves over Finite Fields
We use Eisenstein’s irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y) ∈ GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc := {(x,y)∈GF(q)2 | P(x,y)= c}. 2000 Mathematics Subject Classification. 11T06.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.03.010