The problem of reconstructing a matrix with a specific structure from a partial or total spectral data is known as inverse eigenvalue problem (IEP) which arises in a variety of applications. In this talk, we study a partially described inverse eigenvalue problem of periodic Jacobi matrices and prove some spectral properties of such matrices. The problem involves the reconstruction of the matrix by one eigenvalue of each of its leading principal submatrices and one eigenvector of the required matrix and one more additional piece of information. This talk is joint work with Dr.  S. A. Shahzadeh Fazeli and is based on the papers:

[1] M. Heydari, S. A. Shahzadeh Fazeli, S. M. Karbassi & M. R. Hooshmandasl (2020) On the inverse eigenvalue problem for periodic Jacobi matrices, Inverse Problems in Science and Engineering, 28:9, 1253--1264.

[2] M. Heydari, S. A. Shahzadeh Fazeli, S. M. Karbassi (2019) On the inverse eigenvalue problem for a special kind of acyclic matrices, Applications of Mathematics, Vol. 64, No. 3, 351--366.