222 research outputs found

    Suborthogonality and orthocentricity of matrices

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    AbstractWe present some results on submatrices of orthogonal and unitary matrices and their relation to so called orthocentric matrices. These are then completely characterized

    Quasidirect decompositions of Hankel and Toeplitz matrices

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    AbstractDecompositions, over an algebraically closed field, of a Hankel matrix into a sum of Hankel matrices the sum of the ranks of which is equal to the rank of the original matrix, are completely described. Similar results hold for Toeplitz matrices

    Some remarks on numerical solution of linear problems

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    A deflation formula for tridiagonal matrices

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    summary:An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal

    A note on nonnegative matrices

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    Irreducibility of associated matrices

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    AbstractFor an n by n matrix A, let K(A) be the associated matrix corresponding to a permutation group (of degree m) and one of its characters. Let Dr(A) be the coefficient of xm−r in K(A+xI). If A is reducible, then Dr(A) is reducible. If A is irreducible and the character is identically one, then D1(A) is irreducible. If A is row stochastic and the character is identically one, then Dr(A) is essentially row stochastic. Finally, the results motivate the definition of group induced diagraphs

    Some Inequalities for the Spectrum of a Matrix

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    Spectral radius and Hamiltonicity of graphs

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    Let G be a graph of given order and mu(G) be the largest eigenvalue of its adjacency matrix. We give conditions on mu(G) that imply Hamiltonicity of G and of its complement
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