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We prove the so-called conjecture: for every real-monic polynomial of degree there exists an n by n matrix with sign patternwhose characteristic polynomial is . The proof converts the problem of determining the nonsingularity of a certain Jacobi matrix to the problem of proving the non-existence of a nonzero matrix B that commutes with a nilpotent matrix with sign pattern and has zeros in positions , and for . 相似文献
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One dimensional Dirac operators considered with -potentials and subject to regular boundary conditions (), have discrete spectrum. For strictly regular , the spectrum of the free operator is simple while the spectrum of is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval . Analogous results are obtained for regular but not strictly regular . 相似文献
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LeRoy B. Beasley 《Linear algebra and its applications》2012,436(9):3469-3474
Let be the binary Boolean algebra. The Boolean rank, or factorization rank, of a matrix A in is the smallest k such that A can be factored as an times a matrix. The isolation number of a matrix, A, is the largest number of entries equal to 1 in the matrix such that no two ones are in the same row, no two ones are in the same column, and no two ones are in a submatrix of A of the form . It is known that the isolation number of A is always at most the Boolean rank. This paper investigates for each k, if the isolation number of A is k what are some of the possible values of the Boolean rank of A. 相似文献
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Hyoung Joon Kim 《Journal of Mathematical Analysis and Applications》2012,386(1):110-114
It is well known that if , where A is compact, then T has a nontrivial hyperinvariant subspace. In this paper, we try to solve the hyperinvariant subspace problem for operators which have a compact part. Our main result is that if A is compact, then either or has a nontrivial hyperinvariant subspace. 相似文献
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In this paper we study the existence of distributional solutions of Dirichlet problems whose simplest example is 相似文献
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