منابع مشابه
Congruence of Hermitian Matrices by Hermitian Matrices
Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...
متن کاملPolynomial Extension of Fleck’s Congruence
Let p be a prime, and let f(x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum ∑ k≡r (mod pβ) (n k ) (−1)f (⌊ k − r pα ⌋) , where α > β > 0, n > pα−1 and r ∈ Z. This polynomial extension of Fleck’s congruence has various backgrounds and several consequences such as ∑ k≡r (mod pα) (n k ) a ≡ 0 ( mod p ⌊ n−pα−1 φ(pα) ...
متن کاملSome results on the polynomial numerical hulls of matrices
In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.
متن کاملSome Results on Polynomial Numerical Hulls of Perturbed Matrices
In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.
متن کاملArith . POLYNOMIAL EXTENSION OF FLECK ’ S CONGRUENCE
Let p be a prime, and let f (x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum k≡r (mod p β) n k (−1) k f k − r p α , where α β 0, n p α−1 and r ∈ Z. This polynomial extension of Fleck's congruence has various backgrounds and several consequences such as k≡r (mod p α) n k a k ≡ 0 mod p n−p α−1 ϕ(p α) provided that ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00029-4