Abstract: The problem of reconstructing a pseudo-Jacobi matrix, arising from the discretization and truncation of the Schrödinger equation, is of interest in non-Hermitian quantum mechanics. Also the reconstruction of the Hamiltonian system of an indefinite Toda lattice and the symmetry reduction of the Wess-Zumino-Novikov-Witten model in quantum field theory deserve the attention of physicists and mathematicians. In this talk, the pseudo-Jacobi inverse eigenvalue problem (PJIEP), which concerns the reconstruction from assigned spectral data of a specified pseudo-Jacobi matrix, is investigated.

This talk is based on a joint work with Wei-Ru Xu; Yi Gong and Guo -Liang Chen.

Keywords: inverse eigenvalue problem; pseudo-Jacobi matrices

Homepage: http://www.mat.uc.pt/~bebiano/

Abstract: Two (complex or real) matrices A and B are parallel if there is a complex unit µ such that ∥A + µB∥ = ∥A∥ + ∥B∥. We study linear maps preserving parallel pairs on different matrix spaces such as rectangular matrices, symmetric matrices, skew-symmetric matrices, complex Hermitian matrices. Extensions of the results to infinite dimensional operators are also considered.

The talk is based on joint work with Ming-Cheng Tsai, Taipei University of Technology 10608, Taiwan, (mctsai2@mail.ntut.edu.tw); Yashu Wang, National Chung Hsing University, Taichung 40227, Taiwan, (yashu@nchu.edu.tw); Ngai-Ching Wong, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, (wong@math.nsysu.edu.tw).

Homepage: https://cklixx.people.wm.edu/.