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Positive semidefinite diagonal minus tail forms are sums of squares
By a diagonal minus tail form (of even degree) we understand a real homogeneous polynomial F(x1, . . . , xn) = F(x) = D(x) − T(x), where the diagonal part D(x) is a sum of terms of the form $${b_iExpand
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Young-type inequalities and their matrix analogues
We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove theExpand
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A generalization of a theorem of König
We generalize a theorem of Konig concerning nonnegative integer matrices with constant line sums.
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The Validity of the Marcus - de Oliveira Conjecture for Essentially Hermitian Matrices
Abstract Let X,Y be matrices of spectra x 1 ,…, x n and y 1 ,…, y n , respectively. For a wide class of pairs of essentially Hermitian matrices X,Y , we prove that the determinant of X+Y belongs toExpand
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Optimizers for Sub-Sums subject to a Sum- and a Schur-Convex Constraint with Applications to Estimation of Eigenvalues
A complete solution is presented for the problem of determining the sets of points at which the functions (x1, . . . , xn) → xk + . . . + xl, subject to the constraints M x1 . . . xn m, x1 + x2 + . .Expand
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A combinatorial theorem on the Cartan invariants of the Schur algebra S(B
Abstract We prove an identity for the Cartan invariants of the Schur algebra S(B+) using combinatorial properties of row semistandard λ-tableaux. The problem arose in connection with the constructionExpand
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