Linear Algebra and Its Applications
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.
Higgins, V., & Johnson, C. (2016). Inverse spectral problems for collections of leading principal submatrices of tridiagonal matrices. Linear Algebra and its Applications, 489, 104-122.