A new inverse three spectra theorem for Jacobi matrices

作者：Bai, Yu; Wei, Guangsheng^*

来源：Linear Algebra and Its Applications, 2016, 493: 301-312.

DOI：10.1016/j.laa.2015.12.001

• Jacobi matrix
• Eigenvalue
• Inverse three spectra theorem

This paper deals with an inverse three spectra problem for Jacobi matrices, where the spectrum of the full N x N Jacobi matrix T is prescribed, together with the spectra of two matrices obtained from the principal submatrices of T, denoted by T-1,T-n, and T-n+1,T-N, by modifying the lower right entry of T-1,T-n and the upper left entry of Tn+i,N. Here n satisfying 1 <= n < N is fixed. Denote by Tin and T-1,n,N(-) the modified principal submatrices. We give conditions for three given sets of points to be the spectra of a matrix T and of its two modified principal submatrices T-1,n(-) and T-n+1(+),N to uniquely reconstruct the original matrix T, where the matrix T is a rank 2 perturbation of T-1,n(-) circle plus T-n+1N(+).

• 出版日期2016-3-15
• 单位陕西师范大学