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Inverse spectral problems for collections of leading principal submatrices of tridiagonal matrices
Higgins, Vijay Johnson, Charles
Higgins, Vijay
Johnson, Charles
Abstract
Which assignments from 2n-1 arbitrary, distinct real numbers as eigenvalues of designated leading principal submatrices permit a real symmetric tridiagonal matrix? We raise this question, motivated both by known results and recent work on multiplicities and interlacing equalities in symmetric matrices whose graph is a given tree. Known results are reviewed, a general conjecture is given, and several new partial results are proved. (C) 2015 Elsevier Inc. All rights reserved.
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2016-01-01
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inverse_spectral.pdf
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Mathematics
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10.1016/j.laa.2015.10.004